In the existing software-defined satellite network, the storage space of ternary content addressable memory occupied by the flow table is increasing, and the complex flow entry lookup and matching processes will bring about reduced route forwarding efficiency, which cannot meet the requirements of diverse application requirements. A neural network-based software-defined satellite network intelligent routing framework was proposed. The controller acquired the transmission mode of the data flow by training the neural network, and replaced the flow table with the trained neural network. Based on this framework, an intelligent routing strategy based on Chebyshev neural network was proposed. The switch predicts the forwarding path of data flow according to the service type of data flow to meet the quality of service requirements of satellite network applications. The simulation results show that the proposed routing strategy significantly reduces the occupied storage space of ternary content addressable memory and improves the routing efficiency.