Multiferroic materials with the cross-coupling of magnetic and ferroelectric orders provide a new platform for physics study and designing novel electronic devices. However, the weak coupling strength of ferroelectricity and magnetism is the main obstacle for potential applications. The recent research focuses on enhancing the coupling effect via synthesizing novel materials in a chemical route or tuning the multiferroicity in the physical way. Among them, pressure is an effective method to modify multiferroic materials, especially when the chemical doping has reached its tuning limit. In this work, we systemically studied the multiferroic properties in a hydrogen-bonded metal-organic framework (MOF) [(CH3)2NH2]Ni(HCOO)3 under high pressure. X-ray diffraction and Raman scattering reveal that a structural phase transition occurs in a pressure region of 6-9 GPa, and the crystal structure is greatly modified by pressure. With the ac magnetic susceptibility, pyroelectric current, and dielectric constant measurements, we obtain the multiferroic property evolution under high pressure and create a temperature-pressure phase diagram. Our study demonstrates that the pressure can modify the magnetic superexchange interaction and hydrogen bonding simultaneously in these perovskite-like MOFs. The multiferroic phase region has been expanded to higher temperature due to the pressure-enhanced spin-phonon coupling effect.