A 3D hybrid zinc formate framework, [NH4][Zn(HCOO)(3)], possessing an acs topology, shows a high degree of mechanical anisotropy and negative linear compressibility (NLC) along its c axis. High-pressure single-crystal X-ray diffraction studies and density functional theory calculations indicate that contraction of the Zn-O bonds and tilting of the formate ligands with increasing pressure induce changes in structure that result in shrinkage of the a and b axes and the NLC effect along c.