A resonant quantum magnetoelectric coupling effect has been demonstrated in the multiferroic metal-organic framework of [(CH3)2NH2]Fe(HCOO)3. This material shows a coexistence of a spin-canted antiferromagnetic order and ferroelectricity as well as clear magnetoelectric coupling below TN ≈ 19 K. In addition, a component of single-ion quantum magnets develops below ∼ 8 K because of an intrinsic magnetic phase separation. The stair-shaped magnetic hysteresis loop at 2 K signals resonant quantum tunneling of magnetization. Meanwhile, the magnetic field dependence of dielectric permittivity exhibits sharp peaks just at the critical tunneling fields, evidencing the occurrence of resonant quantum magnetoelectric coupling effect. This resonant effect enables a simple electrical detection of quantum tunneling of magnetization.