The finite element method is developed for 3-D general boundary value problems for a piezoelectric semiconductor with functionally graded material properties. The electron density and electric current are additionally considered in the constitutive equations for piezoelectric semiconductors. A general variation of material properties with Cartesian coordinates is treated in the numerical analyses. The influence of material parameter gradation and initial electron density is investigated in the static case. Numerical results are presented for a 3-D beam under a static and impact mechanical load. Transversely isotropic material properties are considered in this study.