To overcome the false lock or detection missing problems caused by the multiple peaks of the auto-correlation function (ACF) of Binary Offset Carrier (BOC) modulated signal, an acquisition algorithm based on unit correlation for BOC(n,n) signal is proposed in this paper. The local BOC signal is separated into two unit signals, an odd one and an even one. Then a reconstruction of the unit correlation functions between the unit signals and the received BOC signal is performed and M sections of reconstructed correlation function are accumulated according to the non-coherent method, so that this novel acquisition algorithm can not only eliminate the multiple secondary peaks, but also retain the advantage of the narrow correlation main peak. Simulation results show that the acquisition sensitivity of the proposed algorithm is increased 3dBHz compared with the ASPeCT method, and the computation cost is only 41.46% of the ASPeCT method when M=2.