We have developed a superresolution vibrational imaging method by simultaneous detection of Raman and hyper-Raman scattering. Raman and hyper-Raman images obtained with the same laser spot carry independent information on the sample spatial distribution, owing to different signal dependence (linear in Raman and quadratic in hyper-Raman) on the incident light intensity. This information can be quantitatively analyzed to recover the incident light intensity distribution at the focal plane. A superresolution vibrational image is then derived by the constrained deconvolution of the images by the obtained incident light intensity distribution. This method has been applied to a ${\mathrm{TiO}}_2$ nanostructure and the obtained superresolution image was compared with a scanning electron microscopy image. The spatial resolution achieved by the present method is evaluated to be $160\mathrm{nm}$ , which is more than twice better than the diffraction limited resolution.