diff --git a/container_linux_test.go b/container_linux_test.go
index ec02042ad..43c1d6904 100644
--- a/container_linux_test.go
+++ b/container_linux_test.go
@@ -2043,6 +2043,10 @@ func TestShimOOMScore(t *testing.T) {
 	}
 
 	expectedScore := containerdScore + 1
+	if expectedScore > sys.OOMScoreAdjMax {
+		expectedScore = sys.OOMScoreAdjMax
+	}
+
 	// find the shim's pid
 	if cgroups.Mode() == cgroups.Unified {
 		processes, err := cg2.Procs(false)
diff --git a/runtime/v1/shim/client/client.go b/runtime/v1/shim/client/client.go
index e35dafec3..9211c0052 100644
--- a/runtime/v1/shim/client/client.go
+++ b/runtime/v1/shim/client/client.go
@@ -174,6 +174,7 @@ func eaddrinuse(err error) bool {
 
 // setupOOMScore gets containerd's oom score and adds +1 to it
 // to ensure a shim has a lower* score than the daemons
+// if not already at the maximum OOM Score
 func setupOOMScore(shimPid int) error {
 	pid := os.Getpid()
 	score, err := sys.GetOOMScoreAdj(pid)
@@ -181,6 +182,9 @@ func setupOOMScore(shimPid int) error {
 		return errors.Wrap(err, "get daemon OOM score")
 	}
 	shimScore := score + 1
+	if shimScore > sys.OOMScoreAdjMax {
+		shimScore = sys.OOMScoreAdjMax
+	}
 	if err := sys.SetOOMScore(shimPid, shimScore); err != nil {
 		return errors.Wrap(err, "set shim OOM score")
 	}
diff --git a/runtime/v2/shim/util_unix.go b/runtime/v2/shim/util_unix.go
index 2b0d0ada3..9fb7cc573 100644
--- a/runtime/v2/shim/util_unix.go
+++ b/runtime/v2/shim/util_unix.go
@@ -53,6 +53,7 @@ func SetScore(pid int) error {
 
 // AdjustOOMScore sets the OOM score for the process to the parents OOM score +1
 // to ensure that they parent has a lower* score than the shim
+// if not already at the maximum OOM Score
 func AdjustOOMScore(pid int) error {
 	parent := os.Getppid()
 	score, err := sys.GetOOMScoreAdj(parent)
@@ -60,6 +61,9 @@ func AdjustOOMScore(pid int) error {
 		return errors.Wrap(err, "get parent OOM score")
 	}
 	shimScore := score + 1
+	if shimScore > sys.OOMScoreAdjMax {
+		shimScore = sys.OOMScoreAdjMax
+	}
 	if err := sys.SetOOMScore(pid, shimScore); err != nil {
 		return errors.Wrap(err, "set shim OOM score")
 	}
diff --git a/sys/oom_unix.go b/sys/oom_unix.go
index d49d5bc8d..c381e1a7e 100644
--- a/sys/oom_unix.go
+++ b/sys/oom_unix.go
@@ -26,8 +26,12 @@ import (
 	"strings"
 )
 
-// OOMScoreMaxKillable is the maximum score keeping the process killable by the oom killer
-const OOMScoreMaxKillable = -999
+const (
+	// OOMScoreMaxKillable is the maximum score keeping the process killable by the oom killer
+	OOMScoreMaxKillable = -999
+	// OOMScoreAdjMax is from OOM_SCORE_ADJ_MAX https://github.com/torvalds/linux/blob/master/include/uapi/linux/oom.h
+	OOMScoreAdjMax = 1000
+)
 
 // SetOOMScore sets the oom score for the provided pid
 func SetOOMScore(pid, score int) error {
diff --git a/sys/oom_windows.go b/sys/oom_windows.go
index a917ba635..215c171f6 100644
--- a/sys/oom_windows.go
+++ b/sys/oom_windows.go
@@ -16,6 +16,11 @@
 
 package sys
 
+const (
+	// OOMScoreAdjMax is not implemented on Windows
+	OOMScoreAdjMax = 0
+)
+
 // SetOOMScore sets the oom score for the process
 //
 // Not implemented on Windows