The logarithmic quadratic proximal (LQP) regularization is a popular and powerful proximal regularization technique for solving monotone variational inequalities with nonnegative constraints. In this paper,we propose an implementable two-step method for solving structured variational inequality problems by combining LQP regularization and projection method. The proposed algorithm consists of two parts.The first step generates a pair of predictors via inexactly solving a system of nonlinear equations. Then, the second step updates the iterate via a simple correction step. We establish the global convergence of the new method under mild assumptions. To improve the numerical performance of our new method, we further present a self-adaptive version and implement it to solve a traffic equilibrium problem. The numerical results further demonstrate the efficiency of the proposed method.