In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${psi}(t)={frac{t^{p+1}-1}{p+1}}+{frac{1}{sigma}}(e^{{sigma}(1-t)}-1)$, p $in$ [0, 1], ${sigma}{geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+kappa)n^{{frac{1}{p+1}}}lognlog{frac{n}{varepsilon}})$ complexity bound. When p = 1, we have $O((1+2kappa)sqrt{n}lognlogfrac{n}{varepsilon})$ complexity which is so far the best known complexity for large-update methods.