In this talk,  the existence of insensitizing controls for some forward and backward stochastic degenerate parabolic equations are studied, respectively. The key is to transform insensitivity problems into the controllability for some stochastic degenerate cascade parabolic systems. Based on suitable global Carleman estimates for stochastic degenerate parabolic operators, we get the desired controllability results. Moreover,  the controllability of some coupled degenerate parabolic system with different principal coefficients is established.