Using finite element method in spatial direction and classical L1L1 approximation in temporal direction, a fully-discrete scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h2+τ2−α)O(h2+τ2−α) for the original variable in H1H1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where hh and ττ are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results.