Eels can perform both forward and backward undulatory swimming but few studies are seen on how eels propel themselves backward. A computational study on the unsteady hydrodynamicsoof the backward swimming in the eel anguilla anguilla is carried out and presented. A two-dimensional geometric model of the European eel body in its middle horizontal section is appropriately approximated by a NACA0005 airfoil. Kinematic data of the backward and forward swimming eel used in the computational modeling are based on the experimental results of the European eel. Present study provided the different flow field characteristics of three typical cases in the backward swimming, and confirmed the guess of Wu: When the eel swims steadily, the vortex centers of the reversed von Kármán vortex street are aligned approximately. An extensive comparison between the backward and forward swimming further reveals that the controllable parameters, such as frequency, amplitude and wavelength of the traveling wave, have a similar influence on the propulsion performance as in forward swimming. But it is shown that the backward swimming does not be a "reversed" forward swimming one. The backward swimming does show significant discrepancy in the propulsion performance: utilization of a constant-amplitude wave profile enables larger force generation for maneuverability but with much lower propulsive efficiency instead of the linear-increasing amplitude wave profile in the forward swimming. The actual swimming modes eels choose is the best choice associated with their propulsive requirement, as well as their physiological and ecological adaptation.