In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the Linear Complementarity Problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem of the original problem. The proposed approach extends the processability of the larger class of linear complementarity problems and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded. We find the positive tangent direction of the homotopy path. The difficulty of finding a strictly feasible initial point for the interior point algorithm can be replaced appropriately by combining the interior point with the homotopy method. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm.
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