Satellite communication is becoming an indispensable component of the 5G global networks. Considering the unique characteristics of the satellite communications such as long round trip delay, large cell radius and high satellite speed, initial access and handover are necessary to be improved to guarantee the stable communication for 5G-satellite network, which usually use the random access procedure in traditional terrestrial communication and is not suitable for satellite scenario. Therefore, a 2-step random access for 5G-satellite network (TRAS) and a seamless MC-controlled handover for 5G-satellite network (SMHOS) are proposed in this paper. In particular, the access delay can be reduced and the success rate of access can be improved since the access procedure is simplified and the contention occurs only when the UEs select the same Physical Random Access Channel (PRACH) occasion and Physical Uplink Shared Channel (PUSCH) occasion in TRAS. Moreover, in SMHOS, the management center (MC) can predict the handover of the UE and inform the next satellite to send a broadcast message with embedded information about the reserved PUSCH time–frequency resource. The UE can access to the target satellite immediately when the handover occurs, therefore, seamless handover is realized. Simulation results demonstrate the effectiveness of our TRAS and SMHOS.