<p>This article proposes an alternating direction implicit type operator splitting discontinuous Galerkin finite element method to solve a class of two-dimensional time-fractional diffusion equations numerically. Here, the operator splitting method allows us to split the two-dimensional diffusion equation into two separate one-dimensional equations. In both one-dimensional problems, the time-fractional Caputo derivative is discretized over a uniform mesh using the well-known L2-discretization, and the non-symmetric interior penalty discontinuous Galerkin method is used for the discretization of spatial derivatives over a uniform mesh. Stability and error estimate of the proposed fully discrete scheme are addressed. Finally, we give a numerical experiment to validate the theoretical efficiency of the proposed method.</p>