In this talk we consider the discrete maximum principle (DMP) for the weak Galerkin (WG) discretization of a general anisotropic diffusion problem. Brief introduction to DMP and WG will be given. It turns out that the stiffness matrix of the discretization is not an M-matrix in general, and therefore the theory of  M-matrices, which has been commonly used for the study of DMP, cannot be applied. To avoid this difficulty, a reduced system is first obtained by eliminating certain degrees of freedom  and is shown to satisfy DMP under suitable mesh conditions. Then we establish DMP for the full weak Galerkin approximation.Numerical examples, including DMP-compatible mesh generation using BAMG, will be reported. This talk is based on a joint work with Dr. Weizhang Huang.