As the communication mode with the greatest attention and global network coverage, the Low Earth Orbit (LEO) satellite network has the characteristics of low propagation delay, low link loss and handheld terminal. However, with the increasing requirements of user terminals for network latency and bandwidth, the traditional central cloud computing mode no longer has advantages. Therefore, borrowing from the idea of edge computing in terrestrial networks, Orbital Edge Computing (OEC) technology deploys Multi-access Edge Computing (MEC) servers on LEO satellite constellations to meet the growing demand for real-time and reliability of various applications. Based on the above motivations, this paper proposes an OEC Task Allocation (OEC-TA) algorithm based on the greedy strategy in LEO satellite networks for the Walker Delta satellite constellation, which fully utilizes satellite computing resources to provide services to ground users. Then, we analyze the performance of our proposed algorithm in terms of computational cost. Finally, experimental results show that OEC-TA is better than DEC (Double Edge Computing) and random allocation model on average delay and energy consumption reduction. Compared with DEC, our OEC-TA can reduce the average delay and energy consumption up to 10% and 16.5%, respectively.