Abstract: The coupling constraint of noisy intermediate-scale quantum hardware makes most quantum algorithms change quantum bit mapping by inserting additional quantum gates, so that quantum algorithms run directly on the hardware. In order to reduce the quantum circuit running time and improve the quantum circuit fidelity, this paper designs a SWAP-based prospective heuristic quantum circuit mapping algorithm. First, the prospective mechanism is used to consider the front layer information, which improves the stability of the additional gate count results. Secondly, the search strategy is designed to evaluate the physically close candidate SWAP gates to reduce the search space complexity of SWAP gates. Finally, a bidirectional traversal is used to globally consider the gate information of quantum circuits to obtain higher quality initial mappings. The proposed algorithm is suitable for arbitrary coupled quantum hardware architecture, and has the ability to select circuit depth and additional gate number. The experimental results show that compared with the mainstream algorithms A*-based algorithm (Algorithm based on A* search) and SABRE algorithm (SWAP-based BidiREctional heuristic search algorithm), the SPBHA (SWAP-based Prospective Bidirectional Heuristic) algorithm proposed in this paper can reduce the number of additional gates by about 68% and 34%, shorten the circuit execution time, and ensure the reliability of the quantum program results.