Abstract: A distributed pre-coding algorithm was proposed for low earth orbit (LEO) multi-satellite systems with inter-satellite links (ISLs). Due to the complicated on-board calculations for the numerical solutions in traditional pre-coding algorithms and induced unacceptable computational cost and delay in LEO satellite systems, a distributed pre-coding design algorithm was proposed based on the alternating direction method of multipliers (ADMM) to achieve low complexity, high-throughput and the closed-form solutions. In detail, constructing the auxiliary variables and decomposing the problem, the algorithm was arranged to transform the pre-coding design problem into multiple sub-problems and solve them synchronously. And then, providing one constraint item for each sub-problem and exchanging the designed data matrices only via ISLs after each iteration, the algorithm was designed to carry out distributed pre-coding effectively. Simulation results show that the proposed algorithm can achieve a higher beam rate with lower complexity than that achieved with the typical two-step SR maximization algorithm.