The limited connectivity between physical qubits is one of the most important constraints for noisy intermediate-scale quantum (NISQ) computing devices. Quantum circuit mapping makes all qubits in quantum circuits exchange mutually by inserting SWAP gates to satisfy the restricted connectivity constraints of physical devices. In a noisy computing environment, reducing the number of inserted SWAP gates is of great significance to improve the success rate of quantum computing. In order to minimize the number of SWAP gates, a heuristic quantum circuit mapping algorithm is proposed, and then based on the heuristic algorithm and the random search technology, a multi-iterative stochastic optimization model for quantum circuit mapping is proposed. The experimental results show that the method can greatly reduce the number of quantum gates inserted during the quantum circuit mapping process, and effectively reduce the dependence of the resulting physical circuit on the initial mapping.