Summary: This paper is addressed to showing the existence of insensitizing controls for the one-dimensional Cahn-Hilliard type equation with a superlinear nonlinearity. We solve this problem by reducing the original problem to a controllability problem. The crucial point in this paper is an observability estimate for a linearized cascade system of the Cahn-Hilliard type equation. In order to obtain this observability estimate, we establish a global Carleman estimate for a fourth order parabolic operator.