we study the problem of robot path planning in an environment with dynamic obstacles and present a method of local robot path planning with the prediction of the trajectory of an obstacle being a band. First, the time to sample information of an obstacle is determined according to its position within the vision of the robot and the trajectory of the obstacle is predicted based on information above. Different from traditional methods, the predicted trajectory is not a curve, but a band; and then the risk of collision between the robot and the obstacle is evaluated based on the predicted trajectory; finally, for the case of their collision, a mathematical model of local robot path planning is formulated and particle swarm optimization is employed to solve it. We analyze the method above theoretically and conduct simulations. The results confirm that our method decreases the probability of collision between the robot and the obstacle greatly.