A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equa- tions whose merit function is differentiable every where. For the P0-function F, any stationary point of the merit function solves the VI([a, b], F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.
