The method for measuring a motorcycle trajectory accurately using only GPS is demanded in various fields. In GPS measurement of a motorcycle trajectory, both declination of the body and obstacles near the course cause a bad measurement of trajectory. We propose a new algorithm for GPS measurement of a motorcycle trajectory. The missing observation data within a few seconds are interpolated by curve of the second order. In the result, we obtain the trajectory with excellent continuity and stability. In addition, we make the trajectory smooth using extended Kalman filter. We succeeded in getting the trajectory with high accuracy, which is sufficiently continuous. The precision is equal to that of fixed point positioning given sufficient number of available satellites.