BeiDou signals are modulated with a Neumann-Hofman (NH) code of 1 kbps. The frequent bit transitions lead to a sensitivity attenuation of classic acquisition algorithms. In order to increase acquisition sensitivity for weak BeiDou signals, a novel algorithm based on modified zero-padding and differential correlation is proposed. First, a zero-padding method is used to weaken the effect of NH code. Second, the differential coherent delay time is modified to 20 ms to remove the influence of data bit transitions. The integration time is extended to 10 ms to increase acquisition sensitivity. Finally, Monte Carlo simulations and real data tests are conducted to analyse the performance of the proposed algorithm. Simulated results show that the proposed acquisition algorithm outperforms traditional algorithms under a Carrier-to-Noise ratio (C/N0s) of 20~38 dB-Hz. The sensitivity of the proposed algorithm is about 10dB higher than traditional 6 ms repeated search algorithms. Real data test results show that the proposed algorithm outperforms the traditional method with weak signals. This algorithm can remove the effect of NH code and effectively increase the acquisition sensitivity. The proposed algorithm is suitable for acquisition of weak BeiDou signals.