Acquisition of unaided weak Global Positioning System (GPS) signals requires long coherent integration time and thus all the possible navigation data bit combination paths have to be searched. In this paper, to improve the computational efficiency, the Improved Fast Modified Double-Block Zero Padding (IFMDBZP) algorithm using the Optimal Path Search Method (OPSM) is proposed instead of the FMDBZP algorithm using the All Paths Search Method (APSM). The proposed method consists of unlikely data bit combination path elimination by applying the Viterbi algorithm during each coherent integration step to improve the FMDBZP algorithm. The analyses show that the proposed OPSM can reduce the computation calculations and save memory space without suffering any loss compared to the APSM. And the longer the coherent integration time is, the more benefit one can gain from the proposed method. The simulation results also show that the IFMDPZP algorithm using the proposed OPSM has the same acquisition performance as the APSM.