Low earth orbit(LEO)satellite network is an important development trend for future mobile communication systems,which can truly realize the“ubiquitous connection”of the whole world.In this paper,we present a cooperative computation offload-ing in the LEO satellite network with a three-tier com-putation architecture by leveraging the vertical coop-eration among ground users,LEO satellites,and the cloud server,and the horizontal cooperation between LEO satellites.To improve the quality of service for ground users,we optimize the computation offload-ing decisions to minimize the total execution delay for ground users subject to the limited battery capac-ity of ground users and the computation capability of each LEO satellite.However,the formulated problem is a large-scale nonlinear integer programming prob-lem as the number of ground users and LEO satel-lites increases,which is difficult to solve with general optimization algorithms.To address this challenging problem,we propose a distributed deep learning-based cooperative computation offloading(DDLCCO)algo-rithm,where multiple parallel deep neural networks(DNNs)are adopted to learn the computation offload-ing strategy dynamically.Simulation results show that the proposed algorithm can achieve near-optimal per-formance with low computational complexity com-pared with other computation offloading strategies.