When the robot’s movement has process noise,or its closed-loop feedback sensors have specific observation errors,the robot will present significant uncertain movement. The non-deterministic movement state is discribed by the Gaussian distribution which is widespread in nature. The probability theory combing with the robot’s linear control and Kalman filter estimation is used to plan the trajectory and evaluate the Apriori probability distribution. Linear control method is used in combination with Kalman filter to establish error model of Gaussian motion system. Then,all feasible trajectories are assessed by the Gaussian motion model by calculating the probability of avoiding obstacles and arriving at the target. For the optimal trajectory planning,spline method is used to calculate a set of feasible path. Theoretically,all those trajectories can get the aim point and avoid the obstacles. But for the uncertainty of the robot’s behavior,the robot still has the probability of collision and miss the target. Through Gaussian movement prior probability estimates,the trajectory with the maximum probability value is the optimal one under the non-deterministic Gaussian motion state of the robot.