In this paper, we consider two dimensional fractional sub-diffusion equations with mixed derivatives. A high order compact scheme is proposed to solve the problem. We establish a sufficient condition and show that the scheme converges with fourth order in space and second order in time under this condition. We first give an introduction in Chapter 1. In Chapter 2, we proposed the compact scheme. Chapter 3 is devoted to theoretical analysis concerning with stability and convergence. It is then followed by numerical demonstration in Chapter 4. The last section is a brief conclusion of results given by this paper.