In order to adapt to the development trend of lightweight and low-cost low earth orbit (LEO) satellites and meet the demand for rapid laser inter-satellite link establishment, a payload configuration method combining a rotatable laser payload and a fixed laser payload was adopted based on the analysis of inter-satellite laser configuration principles, used for inter-plane link establishment and intra-plane link establishment respectively. A fast inter-satellite link establishment method and process for laser payloads based on in-orbit star calibration, beacon light-assisted link establishment, and optical axis consistency design were introduced. In-orbit experimental data show that the inter-satellite laser payload link establishment time can be less than 30 s, which can achieve stable and continuous inter-satellite laser communication. The study is helpful for promoting the development and large-scale in-orbit application of inter-satellite laser communication.