The incidence of knee injuries during firefighter training is high, but there is a lack of research on predictive factors and risk assessment for such injuries. Biomechanical assessments can provide a better understanding of how the body’s load changes during exercise, which may alter the risk of injury. Ten firefighters were recruited for our study. Each participant completed the FMS test and the single- and double-leg jump tasks. Motion information was collected and musculoskeletal models of the participants were constructed using OpenSim 4.4 to obtain the joint angle and joint moment. The peak GRF and CoM-CoP angle were also calculated. The findings showed a significantly larger PKFM (p = 0.0195), VAFM (p = 0.0039), and peak AP GRF (p = 0.0039) during the single-leg jump. The opposite performance was observed for KFA (p = 0.0098) and MPA (p = 0.0273). A stepwise multiple linear regression analysis was used to explore the relationship between these parameters and both the FMS score and the times of injuries. The risk of injury is higher in the single-leg jump compared to the double-leg jump. The biomechanical parameters of these two jumps can be used to assess sports injuries and to provide methods and references for injury risk monitoring during firefighter occupational training.