Materials with negative linear compressibility (NLC) counterintuitively expand along one specific direction coupled to the volume reduction when compressed uniformly. NLC with a large value is desired for compression and materials science. However, NLC is generally smaller than -20 TPa-1. High-pressure X-ray diffraction experiments reveal that the β-quartz-like InH(BDC)2 generates an extreme NLC (-62.4 TPa-1) by framework hinging. InH(BDC)2 is much safer and lower-cost than Au+/Ag+ and CN--containing materials that dominated the fields of large NLC. This work reconfirms that a negative thermal expansion flexible framework could likely exhibit large NLC. Moreover, a large NLC could be anticipated to arise from β-quartz-like or related frameworks composed of rigid linear ligands and flexible framework angles.