Summary: We analyze a version of the Mizuno-Todd-Ye predictor-corrector interior point algorithm for the \(\mathcal {P}_*(\kappa)\)-matrix linear complementarity problem (LCP). We assume existence of a strictly positive feasible solution. Our version of Mizuno-Todd-Ye predictor-corrector algorithm is generalization of F. A. Potra results [Eur. J. Oper. Res. 143, No. 2, 257–267 (2002; Zbl 1058.90076)] for (LCP) with \(\mathcal{P}_*(\kappa)\)-matrices. To derive complexity result for this algorithm we are using \(\| \mathbf{v}^{-1}-\text\textbf{v}\| \) proximity measure like Potra. Our algorithm is different from the J. Miao’s method [Math. Program. 69, No. 3 (A), 355–368 (1995; Zbl 0844.90097)] in both the used proximity measure and the way of updating the centrality parameter. Our analysis is easier than the mentioned previous results. We also show that the complexity of our algorithm is \(O((1+\kappa)^{\frac{3}{2}}\sqrt{n}L)\).