The acquisition block in the Global Navigation Satellite System (GNSS) receiver is used to provide initial pseudorandom code bias and carrier Doppler estimates of the received signal for the tracking loop. The demand of more accurate tracking loop requires higher resolution on the acquisition block. A variant of classical FFT-based fast acquisition algorithm is proposed, of which the idea is to compress the sequence of sampled signal to shorter sequences. The correlations of the compressed sequences with local replica are processed in parallel. Then the precise code bias is given according to the correlation results. Both analytical results and simulation results indicate that the proposed algorithm can dramatically reduce the computational payload of acquisition while suffering very limited loss in detection probability.