In this paper, we propose a method of tracking and capturing a moving object by a mobile robot. The position of the moving object is acquired from the relation through color-based image information from a 2-DOF active camera mounted on the mobile robot. The direction and rotational angular velocity of the moving object are estimated using a state estimator. A Kalman fiber is used as the state estimator for taking characteristics of robustness against noises and uncertainties included in the input data. After estimating the trajectory of the moving object, we decide on the optimal trajectory and plan the motion of the mobile robot to capture the target object within the shortest distance and time. The effectiveness of the proposed method is demonstrated by the simulations and experiments.