Aiming at the fast C/A code acquisition of GPS software receiver under weak signal conditions, a new fast acquisition algorithm with high sensitivity is proposed. Firstly, the autocorrelation loss and accumulative error of C/A codes are reduced respectively by using the average correlation technique and the carrier frequency error compensation technique. Then, the complexity of coherent cumulative operations is reduced by use of superposition correlation,and the time-consuming of frequency stepping search is decreased by cyclic shift.Experimental results show that the proposed algorithm can realize the acquisition of weak GPS signals, and has moderate computational complexity and high acquisition probability, which is suitable for the high-sensitivity software receiver.