In order to meet the needs of real-time services in the low-orbit communication network, the paper draws on the related research of edge computing technology in the ground broadband network and applies it to the LEO satellite constellation communication network, sinking the processing power of the backend cloud center (CC) to the nodes close to the user terminals, thereby reducing the response delay of the task and the bandwidth consumption of the backhaul network in the LEO constellation networks. This paper proposes a sever selection strategy based on queuing theory and weighting method. For the computing offload requests submitted by frontend users, this strategy first regards the nearest accessing satellite edge computing node as the first choice to offload computing tasks; if it is not qualified, then synthetically consider various factors, such as the total energy consumption of the data transmission and calculation for the request, the load balancing among the computing nodes, and the response delay to the user, etc. These factors for candidate computing nodes are scored separately, and the all-around score is finally used to select the most suitable computation offloading node. Comprehensive simulation experiments show that, compared with another two approaches, the proposed strategy can ensure that user requests are well satisfied, and can reduce the average response delay in the range from 17% up to 34%.