An H1-Galerkin mixed finite element method (MFEM) is discussed for the two-dimensional Ginzburg-Landau equation with the bilinear element and zero order Raviart-Thomas element (Q11 + Q10 × Q01).A linearized Crank-Nicolson fully-discrete scheme is developed and a time-discrete system is introduced to split the error into two parts which are called the temporal error and the spatial error,respectively.On one hand,the regularity of the time-discrete system is deduced through the temporal error estimation.On the other hand,the superconvergent estimates of u in H1-norm and (q) in H(div;Ω)-norm with order O(h2 + τ2) are obtained unconditionally based on the achievement of the spatial result.At last,a numerical experiment is included to illustrate the feasibility of the proposed method.Here,h is the subdivision parameter and τ is the time step.