Improving rotor stability and reducing leakage at various working parts of gas turbines is an important topic that experts and scholars have always pursued. In this article, a new type of hole-diaphragm-labyrinth seal (HDLS) structure is obtained by introducing an additional damping source. The HDLS structure is built by the traditional diaphragm labyrinth seal (DLS) with a single hole added to the diaphragm. The simulation under different working conditions of three different seal structures is carried out by ANSYS Fluent. Subsequently, the tangential force under different whirl frequencies was obtained. Meanwhile, the empirical parameters in Childs’ model of the dynamic performance of rotor-seal structures were obtained. The results show that the HDLS achieved a 71.4% improvement in the direct stiffness coefficient and a 71.8% improvement in the direct damping coefficient of the traditional labyrinth seal. The leakages of HDLS at different rotation speeds were lower than those of DLS by 1.53% and LS by 3.64%. The HDLS can be comprehensively considered the most promising seals among LS, DLS, and HDLS not only by stability but also by mass flow leakage in the rotor system.