Fast acquisition process of weak spread spectrum signals under high-dynamic situation is a key technology in direct sequence spread spectrum (DSSS) communications. Double block zero padding (DBZP) is an effective algorithm, which can search the code phase and Doppler frequency offset parallelly. However, the length of block and the number of blocks are determined by the frequency resolution and Doppler searching range, and their values are fixed, which makes its acquisition performance limited while the Doppler frequency offset is relatively small. Considering the system of direct sequence spread spectrum and shaped-offset quadrature phase-shift keying (SOQPSK) modulation in this paper, a general overlapping multi block zero padding (GOMBZP) algorithm is proposed based on the idea of data subblock overlapping. This method introduces data overlapping and optimizes the combination method of data block in order to improve the acquisition performance as well as ensure the determined frequency resolution and the search range of Doppler frequency offset. Simulation results show that under the relatively small frequency offsets, the acquisition sensitivity of GOMBZP is increased about 1dB compared with DBZP.