Anisotropic magnetoresistance (AMR) of Cr2Ge2Te6 (CGT), a layered ferromagnetic insulator, is investigated under an applied hydrostatic pressure up to 2 GPa. The easy axis direction of the magnetization is inferred from the AMR saturation feature in the presence and absence of the applied pressure. At zero applied pressure, the easy axis is along the c-direction or perpendicular to the layer. Upon application of a hydrostatic pressure>1 GPa, the uniaxial anisotropy switches to easy-plane anisotropy which drives the equilibrium magnetization from the c-axis to the ab-plane at zero magnetic field, which amounts to a giant magnetic anisotropy energy change (>100%). As the temperature is increased across the Curie temperature, the characteristic AMR effect gradually decreases and disappears. Our first-principles calculations confirm the giant magnetic anisotropy energy change with moderate pressure and assign its origin to the increased off-site spin-orbit interaction of Te atoms due to a shorter Cr-Te distance. Such a pressure-induced spin reorientation transition is very rare in three-dimensional ferromagnets, but it may be common to other layered ferromagnets with similar crystal structures to CGT, and therefore offers a unique way to control magnetic anisotropy.