Joint contact forces measured with instrumented knee implants have not only revealed general patterns of joint loading but also showed individual variations that could be due to differences in anatomy and joint kinematics. Musculoskeletal human models for dynamic simulation have been utilized to understand body kinetics including joint moments, muscle tension, and knee contact forces. The objectives of this study were to develop a knee contact model which can predict knee contact forces using an inverse dynamics-based optimization solver and to investigate the effect of joint constraints on knee contact force prediction. A knee contact model was developed to include 32 reaction force elements on the surface of a tibial insert of a total knee replacement (TKR), which was embedded in a full-body musculoskeletal model. Various external measurements including motion data and external force data during walking trials of a subject with an instrumented knee implant were provided from the Sixth Grand Challenge Competition to Predict in vivo Knee Loads. Knee contact forces in the medial and lateral portions of the instrumented knee implant were also provided for the same walking trials. A knee contact model with a hinge joint and normal alignment could predict knee contact forces with root mean square errors (RMSEs) of 165 N and 288 N for the medial and lateral portions of the knee, respectively, and coefficients of determination (R2) of 0.70 and −0.63. When the degrees-of-freedom (DOF) of the knee and locations of leg markers were adjusted to account for the valgus lower-limb alignment of the subject, RMSE values improved to 144 N and 179 N, and R2 values improved to 0.77 and 0.37, respectively. The proposed knee contact model with subject-specific joint model could predict in vivo knee contact forces with reasonable accuracy. This model may contribute to the development and improvement of knee arthroplasty.