Mobile manipulator combines the mobility of mobile platform and the dexterity of manipulator, which has the great application potential in industry scenarios. In practical applications, efficiently planning a path in a given environment is the main objective, but the high degrees of redundancy, which is caused by the coupling of platform and manipulator, will make the planning problem more challenging. Therefore, the motion planning based on the RRT-GoalBias algorithm and path smoothing is proposed in this paper, where the kinematics of mobile manipulator is modeled, and the constraints of configuration and obstacle avoidance are analyzed. Subsequently, the RRT-GoalBias algorithm is applied and modified to generate an initial path for mobile manipulator in a given site, and a novel post-processing algorithm is proposed to smooth and optimize the initial path. Comparative Simulations are carried out with MATLAB and V-REP to verify the effectiveness of the proposed path planning algorithm for mobile manipulator under the given environment.