Judicial review is simply the concrete manifestation of two things express in the Constitution:

(1) the judicial power regarding cases and controversies arising under the Constitution, laws, etc., and

(2) The Constitution’s express limits on what laws Congress has the power to pass.

It's anti-democratic in the sense that Constitutionally-limited government is itself anti-democratic, in that the electre representatives of the people are denied the unlimited power they would have in a parliamentary supremacy model, but not in any other sense.