In this letter, we propose GPS L5 acquisition schemes to detect a fast code phase and improve the accuracy of the Doppler frequency. The proposed approach is based on the code-phase changes which occur during the acquisition processing time originating in the Doppler frequency. The proposed schemes detect a fast code phase within about 1 chip near the estimated code phase and improve the accuracy of the Doppler frequency by up to about 4 times in comparison with the popular Septentrio receiver. The feasibility of the proposed schemes is demonstrated through simulation.