In this paper, we first consider a modified Levenberg–Marquardt method for solving nonlinear equations and show that the method converges superlinearly to a solution of the nonlinear equations under suitable conditions. Then, we reformulate the C-/M-/S-stationarity conditions of mathematical program with complementarity constraints as nonlinear equations so that we may employ the modified Levenberg–Marquardt method to solve these stationarity systems. Preliminary numerical experiments show that the new approach is promising.