Based on the analysis of the influence of residual Doppler on the acquisition of weak global navigation satellite system (GNSS) signals, an acquisition algorithm based on zero forcing (ZF) frequency error correction is proposed. Integrating the frequency correction calculation step of the ZF algorithm with the fast modified double block zero padding (FMDBZP) algorithm organically, the high precision frequency estimation results are obtained; then, the correction terms are introduced to the local oscillator loop in real time. The theoretical analysis and simulation experiments show that the proposed algorithm can improve the acquisition sensitivity significantly. Under given simulation conditions, the proposed algorithm has a 1.2 dB performance improvement compared with that of the FMDBZP algorithm, and the standard deviation captured under the given integral time and the carrier noise ratio is less than 2 Hz.