This paper proposes a skill learning approach for precision assembly robot, aiming to realize efficient skill transfer from teacher to robot through several demonstrations. The framework is designed considering that a skill has multiple controllers and procedures. A complex skill is segmented to an action sequence according to the changes of the teacher's selective attention settings on the multiple system variables. The learning of each action is to select a predefined action class and learn its key parameters from the demonstration data. The action sequence forms a finite state machine. To execute an action, firstly the action instance is generated from the action class and the learned parameters. Then at each time step the action state is updated by the Gaussian mixture model based dynamical system and is sent to the lower level controller as the reference signal, so that the action state evolves towards the target with a specified motion pattern. In this work, the action classes of image feature guided motion and the force constrained motion are proposed based on the multi-camera microscopic vision and 3-dimensional force feedback, respectively, which can be reused in different skills. The proposed approach was validated by the two experiments of the sleeve-cavity assembly and the coil-cylinder assembly.