The rotor is the core component of a gas turbine, and more than 80% of the failures in gas turbines occur in the rotor system, especially during the start-up period. Therefore, the safety assessment of the rotor during the start-up period is essential for the design of the gas turbine. In this paper, the transient equivalent stress of a gas turbine rotor under the cold start-up condition is investigated and the novel tie rod structure is introduced to reduce the equivalent stress. Firstly, a three-dimensional finite element model of the gas turbine rotor is built, and nonlinear contact behaviors such as friction are taken into account. Secondly, the convective heat transfer coefficients of the gas turbine rotor under the cold start-up condition are calculated using thermal dynamic theory. The transient analysis of the gas turbine rotor is conducted considering the thermal load, the centrifugal load, and the pretightening force. The temperature and stress distributions of the rotor under the cold start-up condition are shown in detail. In particular, the generation mechanism of maximum equivalent stress for tie rods and the change tendency of the pretightening force are illustrated in detail. The tie rod holes of the rear shaft and the turbine tie rod are the dangerous locations during the startup period. Finally, a novel tie rod is proposed to reduce the maximum equivalent stress at the dangerous location. The maximum equivalent stress at this location is decreased by 15%. This paper provides some reference for the design of the gas turbine rotor.