Mobile manipulators tasks frequently encompass multiple objectives. For each of these task objectives, there exist numerous potential docking positions. It is a challenge to conduct reasonable multi-targets path planning for mobile manipulators in complex environments. In this paper, we propose a multi-targets path planning method based on manipulability for mobile manipulators to optimize their flexibility while shorting paths lengths. During the node sampling, a study is conducted on the distribution of the robot's manipulability in Cartesian space, allowing for the assessment of the robot's manipulability with respect to the objectives within the docking area. The approach utilizes Gaussian sampling and gradient sampling methods to conduct path point sampling in both free space and the docking-eligible region of the mobile robot, thereby constructing an manipulability roadmap. During the path searching, this study introduces enhancements to the traditional ant colony algorithm by presenting heuristic functions suitable for manipulability constraints and a local-optimal warning strategy. Finally, the proposed path planning method is validated through tests on different simulated maps, showcasing its remarkable adaptability across diverse environments. The method consistently generates low-cost paths while ensuring a high level of manipulability.