Concerning the high time complexity in influence maximization under budget control, a fast influence maximization algorithm, namely BCIM, was proposed. Firstly, a new information dissemination model which propagates the initial nodes for many times was proposed. Secondly, the nodes with high influence ranking value were selected as candidate seeds, and the calculation of node's influence scope was decreased based on the short distance influence. Lastly, only one seed was selected at most in each set of candidate seeds by using the dynamic programming method. The experimental results show that, compared with Random (random algorithm), Greedy_MII (greedy algorithm based on the maximum influence increment) and Greedy_MICR (greedy algorithm based on the maximum of influence increment over cost ratio), the influence scope of BCIM is near to or a bit better than that of Greedy_MICR and Greedy_MII, but much worse than that of Random; the quality of seeds set of BCIM, Greedy_MICR and Greedy_MII is similar, but much better than that of Random; the running time of BCIM is several times of Random, while the running time of the both greedy algorithms are hundreds times of BCIM. In summary, BCIM algorithm can find a more effective seeds set in a short time.