In order to solve the problem of quantum satellite communications handover in low earth orbit (LEO), the algorithm of quantum satellite communication handover in low earth orbit based on entanglement degree computing was proposed. After influence of the distance of quantum satellite and mobile terminal and quantum noise, this algorithm obtained the entanglement of two subsystems when environment have the quantum decoherence in quantum systems and always choose the satellite which have the maximal entangled degree to complete real-time handover. Simulation results show that the handover success rate of this algorithm can achieve more than 95% in both 700 km and 1400 km with some entanglement degree, and it is important that it can achieve smooth handover of quantum satellite. It is important supporting role in building the future global quantum communication system and developing standards.