Most of the space gravitational wave detection missions, such as the Taiji program, use space-based laser interferometer to sense the gravitational waves. However, to obtain the interference signal, the inter-satellite laser acquisition scheme is firstly required to establish the laser link. Traditional acquisition sensors are CCD cameras, which cause a serious heating problem and call for high alignment precision. To avoid these questions, a high-speed, high-precision, fully automatic acquisition scheme with quadrant photodetectors (QPD) is proposed in this paper. Incoherent measurement method of the QPD is introduced to fulfill high-speed acquisition, while a dedicated imaging system is involved for automatic acquisition. Also, an improved differential power sensing (DPS) signal is developed. Combined with the down-sampling algorithm and the match filter algorithm, the acquisition scheme can achieve 1 µrad resolution with total scanning time less than 220 s.