With the rapid development of high-speed railway, the LTE-R communication system has more requirements for the handover success rate. An adaptive handover algorithm based on random suppression in high-speed railway scenario is proposed. The algorithm establishes an elliptic function relationship between the hysteresis threshold and the train speed, so that the hysteresis threshold can be adjusted adaptively with the train speed, which lessens the challenge of high-speed train forward handover. At the same time, the normal distribution random number is introduced to suppress the reverse handover in order to reduce the ping-pong handover rate. Finally, the effectiveness of the algorithm is verified in different scenarios. Simulation results show that compared with the traditional A3 algorithm, the proposed adaptive handover algorithm based on random suppression can improve the handover trigger probability and handover success probability and avoid the increase of ping-pong handover rate.