Eels can swim backward by reversing the direction of the traveling wave along the body. The propulsive mechanism of an eel, angulla angulla, during its self-propelled straight swimming, including forward swimming, braking and switching direction to backward swimming was numerically studied. The problem was reasonably simplified to a loose-coupling problem of fish swimming dynamics and hydrodynamics only in the swimming direction. The approach involved the simulation of the flow by solving the two-dimensional unsteady incompressible N-S equations and the fish motion dynamic problem with Newton's second law. Visualizations of flow fields and vortex structures were performed. The propulsive mechanism and dynamics during each process were investigated and the effects of controllable factors on forward free swimming were discussed.