This study investigates the performance enhancement of a hydrogen pump through an increase in its rotational speed, necessitating a comprehensive safety evaluation of the associated rocket engine from a multi-faceted perspective. Focusing on the root of the impeller, we conduct a simulation analysis to assess its fatigue life under both the original and upgraded operational speeds, employing the Low-High Cycle Combined Fatigue (L-HCCF) methodology. Initially, a sub-modeling technique is utilized to create a detailed mesh of the impeller geometry. Following this, the linear cumulative damage rule is applied to quantify and analyze the composite fatigue life of the impeller. The safety assessment conducted post-speed enhancement yields significant findings: (1) under centrifugal loading, the maximum von Mises stress at the impeller root increases from 722 MPa to 860 MPa; (2) under dynamic loading conditions with liquid hydrogen, the maximum von Mises stress rises from 25 MPa to 33 MPa; and (3) as a result of the performance upgrade, the allowable mission cycles for the first-stage impeller decrease from 5.17 × 104 to 1.01 × 104. Notably, in the absence of atypical vibrational phenomena such as resonance, the design life margin of the impeller remains satisfactory. These findings underscore the critical importance of rigorous safety analyses in the design and optimization of high-performance turbopumps for liquid rocket engines.