In this paper we study primal-dual interior point methods (IPMs) based on a new class of kernel functions which were designed by M. El Ghami, J.B.M Melissen and C. Roos for linear optimization, we extend the functions to second-order cone complementarity(SOCCP). The complexity bound of the method is shown, and the complexity bound of small-update interior-point methods matches the best known complexity bounds obtained for these methods, the complexity bound of large-update interior-point methods is currently the best known bound for primal-dual IPMs.