We calculate the structural, electronic and magnetic properties of the subgroup of Metal–Organic- Frameworks (MOFs) [AmH][M(HCOO)3] (in which AmH+ ¼ organic ammonium cation, M ¼ divalent metal ion) using density functional theory with GGA+U approximation. The optimized structures and magnetic ground states are in good agreement with available experimental results. The electronic structures of these MOFs are obtained at their magnetic ground states. Using hybrid functional method (HSE06), the band gap is 4.33 eV, 4.12 eV, 4.15 eV and 4.78 eV for NH2NH3 +, HONH3 +, CH3CH2NH3 + and NH4 + compounds, respectively. The band gap of NH2NH3 + varies from 2.63 eV (5% compressive strain) to 3.50 eV (+5% tensile strain) at Ueff ¼ 4 eV. It is demonstrated that the band gap of such MOFs can be easily tuned by applying external strain and the AmH+ ligand for the first time. These MOFs all show insulating properties. In addition, such strain engineering may also be useful for enhancing the Neel temperature by changing the distance of magnetic Mn ions. Interestingly, Bader charge analysis indicates that AmH+ is fully ionic suggesting that appropriate arrangement may give rise to polar order associated with the magnetic ordering, these MOFs materials can be considered as potential multiferroics. Finally, this work reveals that both strain and chemical modification are efficient approaches for designing improved and novel MOFs for future applications in photocatalytic, optoelectronic, ferroelectric or multiferroic and electronic device.