Spectrum handover becomes one of the hot topics of Cognitive Radio recently. Spectrum handover happens when the primary users and secondary users collide on the same spectrum hole, and the secondary users need to switch to other spectrum holes to continue the communication. Therefore, the reliability of spectrum Q-learning handover, which is reflected by the quality of service of secondary users and the reduction of interference of primary users, needs deeper research. This paper proposes the scheme of Anticipated Spectrum Handover Scheme (ASHS), which models the primary channel with the consideration of the activity of secondary users based on renewal theory. Secondary users would anticipate the trigger of spectrum handover and select proper spectrum hole as the target one according to the anticipation. The simulation results show that the drop ratio of secondary users is decreased and the frequency of spectrum handovers and passive handovers are decreased.