In this paper, based on the 2-step backward differentiation formula (BDF2 for short) in time and the nonconforming Wilson element in space, a modified Galerkin finite element method named BDF2-MG FEM is proposed to solve the nonlinear complex Ginzburg-Landau equation (GLE for short). On one hand, a modified Ritz projection operator Rh is introduced and analyzed, which plays an important role in getting the unconditional optimal error estimates. On the other hand, a time-discrete system is constructed with the linearized BDF2 and the regularity is derived with the temporal error results. Combining these two aspects, the errors between RhUn and Uhn with order O(h3+h2△t) in L2-norm and O(h2+h2△t) in the modified energy norm are deduced, where h is the subdivision parameter, △t is the time step, Un and Uhn denote the solutions of the time-discrete system and the BDF2-MG FEM respectively. Therefore the boundedness of ‖Uhn‖0,∞ is proven without any restriction on the time-space grid ratio. Furthermore, by using the properties of Rh, unconditional optimal error estimates of order O(h3+(△t)2) in L2-norm and O(h2+(△t)2) in the modified energy norm are obtained directly. It should point out the spatial discrete errors of the BDF2-MG FEM are all one order higher than that of the BDF2 traditional Galerkin finite element method with Wilson element for the GLE. At last, a numerical experiment is presented to verify the validity of the theoretical analysis.