We studied an effect of pressure on the heavy fermion state of YbCo 2 Zn 20 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 1.8 GPa. The super-heavy fermion state in the P c region is found to be strongly destroyed in magnetic fields for H 100 . The field-induced quadrupolar phase, which is most likely realized only for H 111 , is found to be robust even in the antiferromagnetic pressure region.