High magnetic field X-ray diffraction experiments of solid oxygen have been performed at 10 K using DC magnetic fields of up to 5 T as well as pulsed magnetic fields of up to 25 T. The α phase of oxygen exhibits no magnetostriction greater than Δd/d=10-4 at 5 T, where d and Δd denote a lattice plane spacing and its magnetic field variation, respectively. The Δd/d at higher fields of up to 25 T is found to be smaller than 2×10-3. These results contradict the previously reported giant magnetostriction in the α phase where the volume magnetostriction ΔV/V reaches 10-2 at 7.5 T [K. Katsumata, J. Phys.: Condens. Matter 17, L235 (2005)10.1088/0953-8984/17/23/L03].