The flow around and the mechanism of unsteady fluid-dynamic forces acting on an auto-rotating elliptic cylinder were investigated by the experiment using wind tunnel and the two-dimensional numerical simulation. The visualization of flow around the auto-rotating cylinder were carried out by the same rotating frequency and falling velocity as the auto-rotating cylinder. The validity of the computation was confirmed through the comparison with the experimental result. The time variation of the vortex shedding from the cylinder was shown by computational results and it was found that at -110 degree, the three vortices exist in the wake of the cylinder. The drag and lift coefficients acting on the cylinder were estimated by both the numerical result and complex velocity potential theory. It was also found that the phenomenon of the lift coefficient at 0 degree are caused by the effect of the rotation of the cylinder.