Aiming at the problem of slowness of the current meta-heuristic algorithms when solving Travelling Salesman Problem (TSP) in combinatorial optimization problems, a multi-scale adaptive quantum free particle optimization algorithm was proposed based on the inspiration of the wave function in quantum theory. Firstly, the particles representing the city sequences were randomly initialized in the feasible region as the initial search centers. Then, the new solution was obtained by taking each particle as the center to perform the sampling with uniformly distributed function and exchanging the city numbers in the sampling positions. Finally, according to the comparison result of the new solution with the optimal solution in the previous iteration, the search scale was adaptively adjusted, and the iterative search was carried out at different scales until the end condition of the algorithm was satisfied.The algorithm was compared with Hybrid Particle Swarm Optimization (HPSO) algorithm, Simulated Annealing (SA), Genetic Algorithm (GA) and Ant Colony Optimization(ACO) algorithm on TSP. The experimental results show that the multi-scale quantum free particle optimization algorithm is suitable for solving combinatorial optimization problems, and increases the solving speed by over 50% on average compared with the current better algorithms on the TSP datasets.