Unlike terrestrial handover schemes, the handover schemes in 5G satellite–terrestrial integrated network (STIN) face several challenges, such as large propagation delay, complex channel environment, and fast satellite movement. Therefore, the handover schemes designed in the 5G terrestrial network is not suitable for the 5G STIN. In view of this, this paper considers the inter-beam handover problem for the 5G STIN with a low earth orbit satellite and a ground user. We establish the satellite channel model, which includes path loss, rain attenuation, and multi-beam antenna gain. To model the mobile feature of the user, we consider a two-dimensional random walk model. Then, we propose A5 event-based conditional handover (CHO) scheme, time factor-based CHO scheme, and load factor-based CHO scheme to achieve efficient inter-beam handover. Considering that there may be multiple beams that meet the triggering condition in each handover scheme, we also propose three kinds of beam selection schemes, namely random beam selection scheme, maximum power-based beam selection scheme, and minimum distance-based beam selection scheme. To evaluate the performance of the proposed handover schemes, key performance indicators, such as handover frequency, ping-pong handover rate, unnecessary handover rate, handover failure rate, and average transmission rate are analyzed. Simulation results verify the superiority of the proposed handover schemes by comparing them with the benchmark scheme.