We studied an effect of pressure on the heavy fermion state of YbCo2Zn20 under magnetic fields. The critical pressure P-c, where the electronic state changes from the heavy fermion state to the antiferromagnetic state, is estimated to be P-c similar or equal to 1.8 GPa. The super-heavy fermion state in the P-c region is found to be strongly destroyed in magnetic fields for H parallel to < 100 >. The field-induced quadrupolar phase, which is most likely realized only for H parallel to < 111 >, is found to be robust even in the antiferromagnetic pressure region.