This paper proposes two types of the preview algorithms to predict the velocities and joint positions, and deals with a control approach using the preview algorithms for the precise trajectory control. Specifically, a predictor as the form of discrete time state equations is proposed based on the robot dynamics model linearized by the computed toque method. And another state predictor is proposed by the best line fitting in the least square sense, where present joint velocities and positions and several past positions are employed. Then computer simulations are performed for the SCARA robot with two d.o.f to show the validities of the proposed algorithms.