The way geometric frustration in the pyrochlore antiferromagnet HgCr2O4 is relieved by an applied magnetic field is studied by synchrotron X-ray diffraction. The material shows a structural change, from cubic to orthorhombic, at the magnetic transition temperature, T-N similar or equal to 6K, to relieve the geometrical frustration. Below T-N, successive magnetic phase transitions occur in an applied field, from the antiferromagnetic to the half-magnetization plateau phase followed by a transition with a kink in the magnetization. We find that the lattice constant shows discontinuous expansions that coincide with magnetization changes, indicating progressive relief of geometric frustration. We calculate the lattice deformation invoking a magneto-elastic coupling and obtain good agreement between the calculation and our observation.