In this paper, a primal-dual interior point algorithm for solving linear optimization problems based on a new kernel function with a trigonometric barrier term which is not only used for determining the search directions but also for measuring the distance between the given iterate and the µ-center for the algorithm is proposed. Using some simple analysis tools and prove that our algorithm based on the new proposed trigonometric kernel function meets O (√ n log n log nε ) and O (√ n log nε ) as the worst case complexity bounds for large and small-update methods. Finally, some numerical results of performing our algorithm are presented.