This paper presents a volume integral equation (VIE) solver for the forward electromagnetic scattering of 3-D inhomogeneous biaxial anisotropic objects embedded in uniaxial anisotropic media. The optical axes of the objects can be rotated with arbitrary angles. The mixed-order basis functions are employed to discretize the VIE, i.e., the flux densities $(D, B)$ are expanded by the volumetric rooftop basis functions and the vector potentials $(A, F)$ are expanded by the second-order curl conforming basis functions. The weak form of the VIE is formulated by testing it using the same volumetric rooftop basis function and solved by the biconjugate gradient stabilized fast Fourier transform (BCGS-FFT) method. Several numerical simulations of different shapes anisotropic objects are performed and the results are compared with commercial software simulations to validate the accuracy and efficiency of the proposed solver based on different discretization schemes. The major new contribution of this paper is that not only the scatterer but also the background medium is magnetodielectrically anisotropic. Therefore, the dyadic Green’s function for the uniaxial anisotropic background medium is evaluated before solving the VIE.