The crystal structure of glycinium phosphite (GPI) was studied in the pressure range from ambient to 6.5 GPa at 293 K using single-crystal X-ray diffraction. The changes in the unit-cell volume and parameters were continuous and anisotropic. The major compression was observed normal to the direction of the spontaneous polarization that occurs in this structure during a ferroelectric phase transition on cooling, whereas the structural compression along the b axis coinciding with the 21 axis was almost zero. The effect of pressure on the hydrogen bonds linking the H2PO3 tetrahedra into zigzag chains along the c axis was different from that on the hydrogen bonds connecting the glycinium cations with the H2PO3 tetrahedra in the (b × c) plane. The discontinuous changes in the geometries of selected hydrogen bonds at about 1.21 GPa may be evidence of a phase transition, e.g. into an ordered ferroelectric phase (with ordered positions of protons). The anisotropy of compression of GPI in the ferroelectric state (at 0 K) was studied using DFT calculations taking into account dispersive van der Waals interactions. The calculations predicted negative linear compressibility along the b axis.