In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $psi(t)=frac{t^2-1}{2}-{int}^t_1e{^{q(frac{1}{xi}-1)}d{xi}$, $q;{geq};1$. If a strictly feasible starting point is available and the parameter $q;=;log;(1+a{sqrt{frac{2{ au}+2{sqrt{2n{ au}}+{ heta}n}}{1-{ heta}})$, where $a;=;1;+;frac{1}{sqrt{1+2{kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1;+;2{kappa})sqrt{n}log;n;log;{frac{n}{varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1;+;2{kappa})q{sqrt{qn}}log;{frac{n}{varepsilon}})$ iteration complexity.