A trajectory-estimation apparatus and method that can estimate the trajectory of a pen-type optical mouse in a pen-up state. The trajectory-estimation apparatus includes a timer module calculating time for which an optical input device moves in a first state of the optical input device that produces a trajectory, and a trajectory-estimation module estimating the trajectory of the optical input device in a period where a distance between the optical input device and a work surface exceeds a threshold value, based on at least one of the calculated time and a moving speed of the optical input device.