In this work, we reported the observation of a novel planar topological Hall effect (PTHE) in single crystal of Fe3GeTe2, a paradigmatic two-dimensional ferromagnet with strong uniaxial anisotropy. The Hall effect and magnetoresistance varied periodically when the external magnetic field rotated in the ac (or bc) plane, while the PTHE emerged and maintained robust with field swept across the hard-magnetized ab plane. The PTHE covers the whole temperature region below Tc (~150 K) and a comparatively large value is observed at 100 K. Emergence of an internal gauge field was proposed to explain the origin of this large PTHE, which is either generated by the possible topological domain structure of uniaxial Fe3GeTe2 or the non-coplanar spin structure formed during the in-plane magnetization. Our results promisingly provide an alternative detection method to the in-plane skyrmion formation and may bring brand-new prospective to magneto-transport studies in condensed matter physics.