In channel adaptive OFDMA systems, it is important to feed back channel information in a fast, accurate and efficient way to improve the system performance. However, base station requires a large amount of feedback information of channel state information (CSI) in the adaptive channel. In order to reduce the overload of CSI feedback, we propose a feedback scheme which only selects the users scheduled in the next time slot to feed back the channel information according to user mobility. We use adaptive modulation to apply bit rate adaptation depending on user channel condition, where the scheduling time is fixed. By fixing the packet size, scheduling time and feedback period can be fit to different time slots according to user transmission rate. We demonstrate by computer simulation that the proposed scheme can reduce the overload of user feedback with the minimum suppression of the throughput degradation.