The results of the first-principles simulations of water adsorption on (001) surface of both cubic and orthorhombic phases of SrHfO3 crystal are presented. The dissociative and molecular water adsorption is investigated. The role of geometrical and chemical-bonding factors in the relative stability of different adsorption structures is discussed. A symmetry reducing from cubic to orthorhombic is shown to provide more optimal mutual orientation of adsorbate species thus increasing the water adsorption energy on the orthorhombic crystal compared with the cubic one.