By means of spatial quasi-Wilson nonconforming finite element and classical L1L1 approximation, an unconditionally stable fully-discrete scheme for two-dimensional time fractional diffusion equations is established. Moreover, convergence results in L2L2-norm and broken H1H1-norm and the corresponding superclose and superconvergence results in spatial direction in broken H1H1-norm are obtained by use of special properties of quasi-Wilson element. At the same time, the optimal order error estimate in temporal direction is derived by dealing with fractional derivative skillfully. Finally, numerical results demonstrate that the approximate scheme provides valid and efficient way for solving the time-fractional diffusion equation