Power consumption of Global Positioning System (GPS) acquisition is a great challenge for energy-constrained applications. In this work, a metric named acquisition mean computation overhead is proposed to measure the energy cost. A novel multi-peak double-dwell (MP/DD) acquisition method for GPS weak signal is proposed. It adopts multi-peak correlation results as candidates in the first acquisition dwell and selects the largest one as the final acquisition result in the second acquisition dwell. Theoretical analysis and numerical simulation are presented in detail. Meanwhile, the very-large-scale integration (VLSI) implementation of coarse- and fine-grained acquisition engines applied to the proposed method is done. The detection probability and acquisition mean computation overhead are simulated using the Monte-Carlo method, and its mean acquisition power is tested with an actual chip. We fabricated the GPS signal acquisition engine with a 40 nm complementary metal oxide semiconductor (CMOS) process. The simulation results demonstrate that detection probability is promoted from 18% to 67% when signal power is equal to 23 dB/Hz. The acquisition mean computation overhead is reduced greatly by 64%. Measurement results show that the energy consumption of this design is only 21.5% of the conventional double-dwell/maximum (DD/MAX) method.