diff --git a/api/version/version.go b/api/version/version.go
index bd39791a9..ef3c09e7c 100644
--- a/api/version/version.go
+++ b/api/version/version.go
@@ -44,6 +44,9 @@ var (
 	V3_6 = semver.Version{Major: 3, Minor: 6}
 	V3_7 = semver.Version{Major: 3, Minor: 7}
 	V4_0 = semver.Version{Major: 4, Minor: 0}
+
+	// AllVersions keeps all the versions in ascending order.
+	AllVersions = []semver.Version{V3_0, V3_1, V3_2, V3_3, V3_4, V3_5, V3_6, V3_7, V4_0}
 )
 
 func init() {
diff --git a/client/v3/client.go b/client/v3/client.go
index 0c91889fa..10c00f612 100644
--- a/client/v3/client.go
+++ b/client/v3/client.go
@@ -18,11 +18,11 @@ import (
 	"context"
 	"errors"
 	"fmt"
-	"strconv"
 	"strings"
 	"sync"
 	"time"
 
+	"github.com/coreos/go-semver/semver"
 	"go.uber.org/zap"
 	"google.golang.org/grpc"
 	"google.golang.org/grpc/codes"
@@ -32,6 +32,7 @@ import (
 	"google.golang.org/grpc/status"
 
 	"go.etcd.io/etcd/api/v3/v3rpc/rpctypes"
+	"go.etcd.io/etcd/api/v3/version"
 	"go.etcd.io/etcd/client/pkg/v3/logutil"
 	"go.etcd.io/etcd/client/v3/credentials"
 	"go.etcd.io/etcd/client/v3/internal/endpoint"
@@ -475,6 +476,22 @@ func (c *Client) roundRobinQuorumBackoff(waitBetween time.Duration, jitterFracti
 	}
 }
 
+// minSupportedVersion returns the minimum version supported, which is the previous minor release.
+func minSupportedVersion() *semver.Version {
+	ver := semver.Must(semver.NewVersion(version.Version))
+	// consider only major and minor version
+	ver = &semver.Version{Major: ver.Major, Minor: ver.Minor}
+	for i := range version.AllVersions {
+		if version.AllVersions[i].Equal(*ver) {
+			if i == 0 {
+				return ver
+			}
+			return &version.AllVersions[i-1]
+		}
+	}
+	panic("current version is not in the version list")
+}
+
 func (c *Client) checkVersion() (err error) {
 	var wg sync.WaitGroup
 
@@ -496,20 +513,13 @@ func (c *Client) checkVersion() (err error) {
 				errc <- rerr
 				return
 			}
-			vs := strings.Split(resp.Version, ".")
-			maj, min := 0, 0
-			if len(vs) >= 2 {
-				var serr error
-				if maj, serr = strconv.Atoi(vs[0]); serr != nil {
-					errc <- serr
-					return
-				}
-				if min, serr = strconv.Atoi(vs[1]); serr != nil {
-					errc <- serr
-					return
-				}
+			vs, serr := semver.NewVersion(resp.Version)
+			if serr != nil {
+				errc <- serr
+				return
 			}
-			if maj < 3 || (maj == 3 && min < 4) {
+
+			if vs.LessThan(*minSupportedVersion()) {
 				rerr = ErrOldCluster
 			}
 			errc <- rerr
diff --git a/client/v3/client_test.go b/client/v3/client_test.go
index c569d7a3b..f81a1c102 100644
--- a/client/v3/client_test.go
+++ b/client/v3/client_test.go
@@ -24,13 +24,16 @@ import (
 	"testing"
 	"time"
 
+	"github.com/coreos/go-semver/semver"
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 
 	"go.uber.org/zap"
 	"go.uber.org/zap/zaptest"
 
 	"go.etcd.io/etcd/api/v3/etcdserverpb"
 	"go.etcd.io/etcd/api/v3/v3rpc/rpctypes"
+	"go.etcd.io/etcd/api/v3/version"
 	"go.etcd.io/etcd/client/pkg/v3/testutil"
 
 	"google.golang.org/grpc"
@@ -312,6 +315,47 @@ func TestSyncFiltersMembers(t *testing.T) {
 	}
 }
 
+func TestMinSupportedVersion(t *testing.T) {
+	testutil.BeforeTest(t)
+	var tests = []struct {
+		name                string
+		currentVersion      semver.Version
+		minSupportedVersion semver.Version
+	}{
+		{
+			name:                "v3.6 client should accept v3.5",
+			currentVersion:      version.V3_6,
+			minSupportedVersion: version.V3_5,
+		},
+		{
+			name:                "v3.7 client should accept v3.6",
+			currentVersion:      version.V3_7,
+			minSupportedVersion: version.V3_6,
+		},
+		{
+			name:                "first minor version should accept its previous version",
+			currentVersion:      version.V4_0,
+			minSupportedVersion: version.V3_7,
+		},
+		{
+			name:                "first version in list should not accept previous versions",
+			currentVersion:      version.V3_0,
+			minSupportedVersion: version.V3_0,
+		},
+	}
+
+	versionBackup := version.Version
+	t.Cleanup(func() {
+		version.Version = versionBackup
+	})
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			version.Version = tt.currentVersion.String()
+			require.True(t, minSupportedVersion().Equal(tt.minSupportedVersion))
+		})
+	}
+}
+
 func TestClientRejectOldCluster(t *testing.T) {
 	testutil.BeforeTest(t)
 	var tests = []struct {
@@ -323,13 +367,13 @@ func TestClientRejectOldCluster(t *testing.T) {
 		{
 			name:          "all new versions with the same value",
 			endpoints:     []string{"192.168.3.41:22379", "192.168.3.41:22479", "192.168.3.41:22579"},
-			versions:      []string{"3.5.4", "3.5.4", "3.5.4"},
+			versions:      []string{version.Version, version.Version, version.Version},
 			expectedError: nil,
 		},
 		{
 			name:          "all new versions with different values",
 			endpoints:     []string{"192.168.3.41:22379", "192.168.3.41:22479", "192.168.3.41:22579"},
-			versions:      []string{"3.5.4", "3.5.4", "3.4.0"},
+			versions:      []string{version.Version, minSupportedVersion().String(), minSupportedVersion().String()},
 			expectedError: nil,
 		},
 		{
diff --git a/client/v3/go.mod b/client/v3/go.mod
index 518b9de76..45779695a 100644
--- a/client/v3/go.mod
+++ b/client/v3/go.mod
@@ -3,6 +3,7 @@ module go.etcd.io/etcd/client/v3
 go 1.19
 
 require (
+	github.com/coreos/go-semver v0.3.1
 	github.com/dustin/go-humanize v1.0.1
 	github.com/grpc-ecosystem/go-grpc-prometheus v1.2.0
 	github.com/prometheus/client_golang v1.16.0
@@ -18,7 +19,6 @@ require (
 	github.com/benbjohnson/clock v1.1.0 // indirect
 	github.com/beorn7/perks v1.0.1 // indirect
 	github.com/cespare/xxhash/v2 v2.2.0 // indirect
-	github.com/coreos/go-semver v0.3.1 // indirect
 	github.com/coreos/go-systemd/v22 v22.5.0 // indirect
 	github.com/davecgh/go-spew v1.1.1 // indirect
 	github.com/gogo/protobuf v1.3.2 // indirect