Path planning of mobile robot has a purpose to design an optimal path from an initial position to a target point. Minimum driving time, minimum driving distance and minimum driving error might be considered in choosing the optimal path and they are correlated to each other. In this paper, an efficient driving trajectory is planned in a real situation where a mobile robot follows a moving object. Position and distance of the moving object are obtained using a web camera; the rotation angular and linear velocities are estimated using Kalman filters to predict the trajectory of the moving object. Finally the mobile robot follows the moving object using a single curvature trajectory by estimating trajectory of the moving object. Using the estimation by Kalman filters and the single curvature in the trajectory planning, the total tracking distance and error rate have been saved about 7 %.