We propose a weak Galerkin (WG) finite element method for 2- and 3-dimensional convection-diffusion-reaction problems on conforming or nonconforming polygon/polyhedral meshes. The WG method uses piecewise-polynomial approximations of degree $k(k\ge 0)$ for both the scalar function and its trace on the inter-element boundaries. We show that the method is robust in the sense that the derived a priori error estimates is uniform with respect to the coefficients for sufficient smooth true solutions. Numerical experiments confirm the theoretical results.