Magnetization of a single crystalline Ce3Pd20Si6 was measured at low temperatures down to 90 mK in fields up to 11 T for the three principal directions [100], [110], and [111]. For all directions, two transitions were observed in the temperature variation of the magnetization M(T) at 0.2 T; a broad peak at 0.28 K associated with a phase-III transition, and an upward bending at similar to 0.5 K due to a phase-II ordering from the paramagnetic state (phase-I). The latter critical temperature TI-II is found to be strongly enhanced in magnetic fields B, depending on the field direction, and TI-II(B) becomes highly anisotropic. These results suggest that phase-II is an antiferroquadrupole state originated from a Gamma(8) ground state. By contrast, no appreciable anisotropy is found in the phase-III state. At 90 mK, phase-III collapses by applying a field of similar to 0.63 T for all directions. Above this field, the magnetization curve M(B) becomes strongly anisotropic. The magnetization value per Ce in the phase-I region at 90 mK is apparently smaller than the Gamma(8) moment, indicating that either 8c or 4a site has a Gamma(7) ground state.