The overall performance of P2P-based file sharing applications is becoming increasingly important. Based on the Adaptive Resource-based Probabilistic Search algorithm (ARPS), which was previously proposed by the authors, a novel probabilistic search algorithm with QoS guarantees is proposed in this letter. The algorithm relies on generating functions to satisfy the user's constraints and to exploit the power-law distribution in the node degree. Simulation results demonstrate that it performs well under various P2P scenarios. The proposed algorithm provides guarantees on the search performance perceived by the user while minimizing the search cost. Furthermore, it allows different QoS levels, resulting in greater flexibility and scalability.