For the 5G-R wireless communication system of the next-generation high-speed railway, there is a problem of single algorithm consideration when handover is carried out. In high-speed environment, it is easily affected by handover risk, which leads to the problem of low handover success. To solve the above problems, this study proposed a next-generation high-speed railway handover decision algorithm, which is based on improved Criteria Importance through Intercrieria Correlation and Technology for Order Preference by Similarity to an Ideal Solution (CRITIC-TOPSIS) theory. Firstly, considering the factors of reference signal receiving power (RSRP), reference signal receiving quality (RSRQ), and co-frequency interference, an improved CRITIC-TOPSIS multi-attribute joint handover decision method is proposed, which overcomes the problem of single consideration of handover. Then, a handover risk assessment model based on prospect theory is constructed, and the handover risks of trains triggered at different positions are analyzed. Finally, the comprehensive utility value of train handover is obtained by normalization, and the optimal handover position is recommended according to the comprehensive utility value, so as to complete the handover. The experimental results show that the success rate of train handover exceeds 99.5% in viaduct, urban area, open area, and mountainous area. In addition, under different operation scenarios, when the train runs at a speed of 200 km/h to 500 km/h, the handover success rate can be between 99.51% and 99.68%. The proposed method can meet the requirement that the success rate of quality of service (QoS) of 5G-R wireless communication system is greater than 99.5%. The research results provide a theoretical reference for the evolution of the next-generation 5G-R high-speed railway system.