diff --git a/spec/ruby/core/process/setpriority_spec.rb b/spec/ruby/core/process/setpriority_spec.rb
index d3be02eb6d..118482eb4e 100644
--- a/spec/ruby/core/process/setpriority_spec.rb
+++ b/spec/ruby/core/process/setpriority_spec.rb
@@ -29,11 +29,26 @@ describe "Process.setpriority" do
     end
 
     as_superuser do
-      it "sets the scheduling priority for a specified user" do
-        p = Process.getpriority(Process::PRIO_USER, 0)
-        Process.setpriority(Process::PRIO_USER, 0, p + 1).should == 0
-        Process.getpriority(Process::PRIO_USER, 0).should == (p + 1)
-        Process.setpriority(Process::PRIO_USER, 0, p).should == 0
+      p = Process.getpriority(Process::PRIO_USER, 0)
+      # The nice value is a value in the range -20 to 19.
+      # This test tries to change the nice value to +-1, so it cannot run if p == -20 || p == 19.
+      if -20 < p && p < 19
+       begin
+         # Check if we can lower the nice value or not.
+         #
+         # We are not always able to do it even as a root.
+         # Docker container is not always able to do it depending upon the configuration,
+         # which cannot know from the container itself.
+          Process.setpriority(Process::PRIO_USER, 0, p - 1)
+          Process.setpriority(Process::PRIO_USER, 0, p)
+
+          it "sets the scheduling priority for a specified user" do
+            Process.setpriority(Process::PRIO_USER, 0, p + 1).should == 0
+            Process.getpriority(Process::PRIO_USER, 0).should == (p + 1)
+            Process.setpriority(Process::PRIO_USER, 0, p).should == 0
+         end
+       rescue Errno::EACCES
+       end
       end
     end
   end