<p>In this paper, we propose an accelerated derivative-free projection method for the nonlinear complementarity problem, which is formulated by solving its equivalent transformation based on the Fischer-Burmeister function. For the resulting system of nonlinear monotone equations, a spectral three-term hybrid derivative-free projection method is presented. The search direction of our method updates the conjugate parameter by approximating the memoryless BFGS formula, while determining the spectral parameter through the quasi-Newton equation and the double-constraint technique to ensure that it satisfies both the sufficient descent and the trust region property without relying on the line search. To accelerate convergence, a novel accelerated strategy is designed based on the convex combination of two sequences of iteration points. Incorporating the proposed accelerated strategy and the adaptive line search, we establish the global convergence of the proposed method without requiring the mapping to be Lipschitz continuous or smooth. Preliminary numerical experiments indicate that our method outperforms three existing approaches and is competitive with the specialized solver in solving nonlinear complementarity problems of varying scales, particularly in terms of computation time and the number of iterations.</p>