Navigation and obstacle avoidance are essential for mobile robots. In the dynamic environment, the obstacles may move with varying velocities. It is thus crucial to develop an effective scheme for moving obstacle avoidance. Motivated by this, in this paper, we propose such a scheme based on parametric trajectory planning. With the conditions for collision avoidance formulated as the constraints, a feasible collision-free trajectory is then derived by solving an unconstrained optimization problem. The corresponding control torques for robot governing is calculated using the dynamic model and derived trajectory, with the information about the obstacle not known a priori. Simulations are performed to demonstrate the efficiency of the proposed approach.