For sensitivity enhancement, the general assisted-GPS acquisition method adopts not only the coherent accumulation technique but also the non-coherent accumulation technique since the long coherent accumulation period increases the number of frequency search cells. But the non-coherent accumulation technique causes tile squaring loss, which is a dominant factor among the acquisition losses of assisted GPS dealing with weak GPS signals. This paper derives the squaring loss of the previous assisted-GPS acquisition method and proposes an assisted-GPS acquisition method for solving the problem of squaring loss in weak signal environment. In this paper, it is explained that the proposed assisted-GPS acquisition method prevents the squaring loss using a coupled coherent accumulation technique and the number of search cells of the proposed assisted-GPS acquisition method is much smaller than that of the previous assisted-GPS acquisition method. Finally, through the simulation by the GPS simulator, the acquisition success rate of the proposed assisted-GPS acquisition method is compared with that of the previous assisted-GPS acquisition method and the acquisition improvements are shown in weak signal environment.