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For Peer-to-Peer (P2P) streaming services in mobile networks, the selection of appropriate neighbour peers from candidate peers with demanding data is an important approach to improve Quality-of-Service (QoS). This paper proposes a novel Effective Capacity Peer Selection (ECPS) scheme based on effective capacity. In the ECPS scheme, the neighbour peer selection problem was modeled using the Multiple Attribute Decision Making (MADM) theory, which considered multiple factors of candidate peers, including Signal to Interference and Noise Ratio (SINR), residency time, power level, security, moving speed, and effective capacity. This model could increase the suitability of ECPS for wireless mobile environments. Then, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was used to solve the MADM problem and identify the preferred neighbour peers. Simulation results show that the ECPS scheme can improve the network throughput, reduce packet delay by about 82%, and almost double the packet delivery ratio of the mobile P2P streaming service.