In this paper, we propose a second-order corrector interior-point algorithm for solving P * (κ)-linear complementarity problems. The method generates a sequence of iterates in a wide neighborhood of the central path introduced by Ai and Zhang. In each iteration, the method computes a corrector direction in addition to the Ai-Zhang direction, in an attempt to improve performance. The algorithm does not depend on the handicap κ of the problem, so that it can be used for any P * (κ)–linear complementarity problems. It is shown that the iteration complexity bound of the algorithm is O (1 + κ) 3 √ nL. Some numerical results are provided to illustrate the performance of the algorithm.