In this paper, we propose a weighted short-step primal-dual interior point algorithm for solving monotone linear complementarity problem (LCP). The algorithm uses at each interior point iteration a full-Newton step and the strategy of the central path to obtain an \(\epsilon \)-approximate solution of LCP. This algorithm yields the best currently well-known theoretical complexity iteration bound, namely, \(O(\sqrt{n}\log \frac{n}{\epsilon })\) which is as good as the bound for the linear optimization analogue. The implementation of the algorithm and the algorithm in Wang et al. (Fuzzy Inform Eng 54:479–487, 2009) is done followed by a comparison between these two obtained numerical results.