Aiming at the problem of satellite power limitation, this paper proposes a distributed multi-satellite cooperative transmission (DMCT) scheme based orthogonal time frequency space (OTFS) for low earth orbit (LEO) satellite networks to achieve downlink power and transmission performance enhancement. Firstly, we construct the DMCT system model and channel model. Through theoretical analysis, it is found that the dynamic change of phase difference between each data stream from cooperative satellite cluster arriving at the terminal will cause serious time-varying fast fading. To this end, we design the OTFS transmission model for DMCT systems, and present the subspace pursuit (SP) channel estimation method and message passing (MP) data detection method taking advantage of the sparsity of the DMCT channel. Simulation results show that the proposed scheme can significantly enhance downlink power and transmission performance.