A complete set of scattering-state solutions of a Bethe-Salpeter equation is obtained in this paper. This equation is the one for which Wick and Cutkosky succeeded to obtain the bound-state solutions. For bound-state solutions, they have found the same degeneracy as that of the non-relativistic hydrogen atom. This result is very suggestive for the present case, and indeed the scattering-state solutions are obtained without decomposing them into partial waves as is the case for Rutherford scattering. Adopting the integral transformation method, the four dimensional integral equation is reduced to a simple ordinary differential equation. It is interesting to see that this equation is identical with Cutkosky's one for n = 0. Finally by a close inspection of the resulting equation and boundary condition, it is shown that the virtual-state solutions, if any, can be obtained by modifying the inhomogeneous boundary condition for scattering states into a homogeneous one. Furthermore, it is proved that an isolated virtual level, if it really exists, gives rise to a resonance scattering.