For the navigation satellite receiver technology, the weak signal acquisition is the key to improve the receivers' sensitivity. According to the characteristics of the weak signal, long duration correlation integral is the classic method. Unfortunately, the duration is always limited to 10ms for that navigation bit rate is 50bps. In this paper, a dichotomy-based acquisition algorithm is proposed to extend integration duration to 19ms. Meanwhile, to reduce its computation complexity, the convolution operation is replaced by summation for its potential linear relation in the special time. Theoretical analysis and simulated result proves that the proposed algorithm can improve receivers' sensitivity and reduce its computation.