The establishment of a laser link between satellites, i.e., the acquisition phase, is a key technology for space-based gravitational detection missions, and it becomes extremely complicated when the long distance between satellites, the inherent limits of the sensor accuracy, the narrow laser beam divergence and the complex space environment are considered. In this paper, we investigate the laser acquisition problem of a new type of satellite equipped with two two-degree-of-freedom telescopes. A predefined-time controller law for the acquisition phase is proposed. Finally, a numerical simulation was conducted to demonstrate the effectiveness of the proposed controller. The results showed that the new strategy has a higher efficiency and the control performance can meet the requirements of the gravitational detection mission.