Numerical simulations are used to investigate the hydrodynamic benefits of body–fin and fin–fin interactions in a fish model in carangiform swimming. The geometry and kinematics of the model are reconstructed in three-dimensions from high-speed videos of a live fish, Crevalle Jack (Caranx hippos), during steady swimming. The simulations employ an immersed-boundary-method-based incompressible Navier–Stokes flow solver that allows us to quantitatively characterize the propulsive performance of the fish median fins (the dorsal and the anal fins) and the caudal fin using three-dimensional full body simulations. This includes a detailed analysis of associated performance enhancement mechanisms and their connection to the vortex dynamics. Comparisons are made using three different models containing different combinations of the fish body and fins to provide insights into the force production. The results indicate that the fish produces high performance propulsion by utilizing complex interactions among the fins and the body. By connecting the vortex dynamics and surface force distribution, it is found that the leading-edge vortices produced by the caudal fin are associated with most of the thrust production in this fish model. These vortices could be strengthened by the vorticity capture from the vortices generated by the posterior body during undulatory motion. Meanwhile, the pressure difference between the two sides of posterior body resulting from the posterior body vortices (PBVs) helps with the alleviation of the body drag. The appearance of the median fins in the posterior region further strengthens the PBVs and caudal-fin wake capture mechanism. This work provides new physical insights into how body–fin and fin–fin interactions enhance thrust production in swimming fishes, and emphasizes that movements of both the body and fins contribute to overall swimming performance in fish locomotion.