In this paper, we ¯rst present a brief review about the fea- sible interior-point algorithm for P¤(·)-horizontal linear comple- mentarity problems (HLCPs) based on new directions. Then we present a new infeasible interior-point algorithm for these prob- lems. The algorithm uses two types of full-Newton steps which are called feasibility steps and centering steps. The algorithm starts from strictly feasible iterations of a perturbed problem, and feasibility steps ¯nd strictly feasible iterations for the next perturbed problem. By accomplishing a few centering steps for the new perturbed problem, we obtain strictly feasible iterations close enough to the central path of the new perturbed problem and prove that the same result on the order of iteration complex- ity can be obtained.