When considering earth curvature effect, airplane′s longitude, latitude and heading angles are changing in cruising flight condition and simulation using these parameters is complex. Euler angles are introduced to represent the position and heading information of plane and it can directly reflect flying path characteristics, thus the calculation is simple and convenient, especially while the airplane is in steady flying conditions there is only one parameter varying. Euler parameters, the longitude, latitude, and heading angle convert conveniently according to spherical geometry. Euler parameters of the turning, crossing, tracing processes are deducted. The effeciency and convenience in representation of position, heading and variation by Euler parameters are validated by examples.