Bilinear saddle point problem has numerous applications in signal and image processing, machine learning, statistics, high dimensional data analysis, and so on, which be solved efficiently by primal dual algorithms (PDA). By using sequence linear combination, a novel first-order primal-dual algorithm is presented for solving the bilinear saddle point problem. The proposed method improves the Chambolle-Pock PDA and can be seems as a modification of Arrow-Hurwicz method, which combines the linear combination with classic extrapolation technology in subproblems. An $\mathcal{O}(1/N)$ ergodic convergence rate result is derived based on the primal-dual gap function, where $N$ denotes the number of iterations. The preliminary numerical results on the nonnegative least-squares and Lasso problems, with comparisons to some state-of-the-art relative algorithms, demonstrate the efficiency of the proposed algorithm.