The complex Hessian equation is a class of important fully nonlinear geometric elliptic equations which can be viewed as an intermediate case between the Laplacian equations and the complex Monge-Ampere equations. In this talk, we will talk about some a priori estimates for a complex Hessian equation motivated from Fu-Yau’s generalization of the Strominger system. This is a joint work with D. Phong and S. Picard.