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Linear variational inequality is a uniform approach for some important problems in optimization problems and equilibrium problems. In this paper, a neural network for solving a class of extended linear variational inequality is presented based on the projection method. No parameter is involved in the proposed neural network, its structure is very simple and it can be implemented in simple hardware when the feasible region is simple. The proposed neural network can be used to solve a broad classes of optimization problems and some existing models for solving ordinary linear variational inequalities can be derived from it. The proposed neural network is proved to be Lyapunov stable and converge asymptotically to an exact solution of the problem. The feasibility and effectiveness of the proposed network are confirmed by numerical simulations.