A structure and equation of the state of δ-AlOOH has been studied at room temperature, up to 29.35 GPa, by means of single crystal X-ray diffraction in a diamond anvil cell using synchrotron radiation. Above ~10 GPa, we observed a phase transition with symmetry changes from $P{2}_{1}nm$ to $Pnnm$. Pressure-volume data were fitted with the second order Birch-Murnaghan equation of state and showed that, at the phase transition, the bulk modulus (K₀) of the calculated wrt 0 pressure increases from 142(5) to 216(5) GPa.