This paper presents a numerical method to evaluate the electromagnetic scattering from arbitrarily shaped three-dimensional inhomogeneous bianisotropic bodies by using a generalized transition matrix. A generalized transition matrix defined on the reference surface containing the scatterer describes the relationships between the rotated tangential components of incident fields and the rotated tangential components of scattered fields on the reference surface. The method of moments technique is applied to obtain a numerical solution to the surface integral equations in this problem. Compared to methods based on volume integral equations, the generalized transition matrix based on surface integral equations is efficient to represent the scattering characteristics of the inhomogeneous bianisotropic bodies. Some numerical results are also provided to verify the method.