diff --git a/math.c b/math.c
index 0b15ba7056..509cd46ef2 100644
--- a/math.c
+++ b/math.c
@@ -689,7 +689,14 @@ rb_math_sqrt(VALUE x)
 static VALUE
 math_cbrt(VALUE unused_obj, VALUE x)
 {
-    return DBL2NUM(cbrt(Get_Double(x)));
+    double f = Get_Double(x);
+    double r = cbrt(f);
+#if defined __GLIBC__
+    if (isfinite(r)) {
+	r = (2.0 * r + (f / r / r)) / 3.0;
+    }
+#endif
+    return DBL2NUM(r);
 }
 
 /*
diff --git a/test/ruby/test_math.rb b/test/ruby/test_math.rb
index f226287442..5cc12bcfeb 100644
--- a/test/ruby/test_math.rb
+++ b/test/ruby/test_math.rb
@@ -202,6 +202,7 @@ class TestMath < Test::Unit::TestCase
     check(3, Math.cbrt(27))
     check(-0.1, Math.cbrt(-0.001))
     assert_nothing_raised { assert_infinity(Math.cbrt(1.0/0)) }
+    assert_operator(Math.cbrt(1.0 - Float::EPSILON), :<=, 1.0)
   end
 
   def test_frexp