Autonomous planning is a significant development direction of the space manipulator, and learning from demonstrations (LfD) is a potential strategy for complex tasks in the field. However, separating control from planning may cause large torque fluctuations and energy consumptions, even instability or danger in control of space manipulators, especially for the planning based on the human demonstrations. Therefore, we present an autonomous planning and control strategy for space manipulators based on LfD and focus on the dynamics uncertainty problem, a common problem of actual manipulators. The process can be divided into three stages: firstly, we reproduced the stochastic directed trajectory based on the Gaussian process-based LfD; secondly, we built the model of the stochastic dynamics of the actual manipulator with Gaussian process; thirdly, we designed an optimal controller based on the dynamics model to obtain the improved commanded torques and trajectory, and used the separation theorem to deal with stochastic characteristics during control. We evaluated the strategy with locating pre-screwed bolts experiment by Tiangong-2 manipulator system on the ground. The result showed that, compared with other strategies, the strategy proposed in this paper could significantly reduce torque fluctuations and energy consumptions, and its precision can meet the task requirements.