Platform position maintaining is a major challenge for the airship or aircraft based High Altitude Platform (HAP) communication systems. The platform maintaining a stationary position will introduce a high price. Hence, a position cylinder is suggested for the position maintaining of the platform. This paper derives the computation formula for the maximum distance of the HAP horizontal displacement when a fixed pointing antenna is adopted at the terminal, and simultaneously the handover probability in a cellular of the service area under limited and un-limited average call durations is analyzed. The study results show that the maximum distance for the HAP horizontal displacement increases with the user beam-width. Under the condition of the same beam-width, the higher the altitude of the platform, and the smaller the maximum distance for the platform displacement is required. Moreover, the horizontal displacement can only generate handover in the area near the edge of the cellular. The calls which are nearer to the cell edge have higher handover probability. The average handover probability increases with the maximum distance for the HAP displacement. The larger the HAP displacement during the call duration, the greater the average handover probability is. When the call duration time and the platform speed tend to infinite, the handover probability reaches to the maximum value.