In this paper we propose new primal-dual interior point algorithms for $P_*(kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2kappa)n^{frac{9}{14}};log;frac{n{mu}^0}{epsilon}$) for large-update and $O((1+2kappa)sqrt{n}logfrac{n{mu}^0}{epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.