Dental implants made of functionally graded biomaterials (FGBM) have been receiving increasing attention due to their unique advantage of being able to simultaneously satisfy biocompatibility, strength, corrosion resistance, etc., which a single composition with a uniform structure cannot satisfy. This paper investigates the biomechanical behavior of a threaded FGBM dental implant/surrounding bone system under static and harmonic occlusal forces by using a three-dimensional finite element method. The implant is a mixture of a bioceramic and a biometal with a smooth gradient in both the material composition and properties in the longitudinal direction. The interaction of the implant and the supporting bone tissues is considered. Three contact conditions at the implant-bone interface are used to model different osseointegration stages. A comprehensive parametric study is conducted to highlight the influence of the material properties, the volume fraction index, the occlusal force orientation, and the osseointegration quality on the maximum von-Mises stress, deformation distribution, natural frequencies, and harmonic response.