In this paper, we study the Cauchy-Neumann problem for parabolic type and Monge-Ampere type equations. By establishing an anxiliary function, using the methods of the properity at the maximum point and cauchy inequality, we prove the global gradient estimates for second order derivatives. And by using the general theory of parabolic equations, we obtain that such solution exists for all times under smoothness and regularity conditions, which generalizes the results of parabolic type and Monge-Ampere type eq...