In this paper we propose new large-update primal-dual inte-rior point algorithms for $P_*(kappa)$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function$psi(t)=frac{t^{p+1}-1}{p+1}+frac{e^{frac{1}{t}}-e}{e}$,$p{in}$[0,1]. We showed that if a strictly feasible starting point is available, then the algorithm has $O((1+2kappa)(logn)^{2}n^{frac{1}{p+1}}logfrac{n}{varepsilon}$ complexity bound.