We studied the heavy fermion compound YbCo2Zn20 with an electronic specific heat coefficient gamma similar or equal to 8000 mJ/(K-2.mol) by measuring the de Haas-van Alphen (dHvA) oscillation, Hall effect, magnetic susceptibility, and magnetization at ambient pressure, as well as the electrical resistivity in magnetic fields of up to 320 kOe and at pressures of up to 5 GPa. The detected Fermi surfaces are small in volume, reflecting the small Brillouin zone based on the large cubic lattice constant a = 14.005 angstrom. The cyclotron effective masses, which were determined from the dHvA experiment, are found to be markedly reduced in magnetic fields. In other words, the detected cyclotron masses of 2.2-8.9 m(0) (m(0): the rest mass of an electron) at H-av = 117 kOe are enhanced to 100-500 m(0) at 0 kOe. By applying pressure, the heavy fermion state disappears at P-c similar or equal to 1.8 GPa and orders antiferromagnetically for P > P-c. The field-induced antiferroquadrupolar phase, which is observed only for H parallel to < 111 > in the magnetic field range from H-Q = 60 kOe to H-Q' = 210 kOe, is found to shift to lower magnetic fields and merge with theantiferromagnetic phase at 4.5 GPa.