With a focus on the issue of path planning for mobile robots, a genetic ant-colony fusion algorithm is proposed based on pm$3\sigma$ normal probability interval. Given the low quality of the initial population randomly generated by the traditional genetic ant-colony fusion algorithm, an initial population optimization and deletion operator is proposed. Because of the premature convergence of the traditional genetic ant-colony fusion algorithm, a population division mechanism with the fitness value of $\pm3\sigma$ normal probability interval, as well as a family hybrid crossover operator, is proposed. To improve the quality of the generated path after a random mutation, a hybrid mutation strategy is proposed. A global path-planning algorithm and a local path-planning algorithm(the dynamic window method are combined to form a complete mobile robot motion plan. The experimental analysis using the Matlab simulation platform and the robot operating system (ROS) verifies the effectiveness of the proposed algorithm in paper to solve the path-planning problem of mobile robots.