High-pressure Raman scattering experiments were performed on the zircon-type RCrO4 (R=Nd, Dy) compounds with the space group I41/amd by using diamond anvil cell techniques at room temperature. These two compounds exhibit similar Raman behaviors. Pressure-induced structural phase transitions were observed at the onset of 1.3 and 4.1 GPa for R=Nd and Dy, respectively. Moreover, pressure-released Raman spectra indicate that the structural transitions are irreversible. The high-pressure new phases were convincingly confirmed to be the scheelite structure in I41/a symmetry based on the same Raman vibrations between the pressure-released DyCrO4 and the scheelite-type DyCrO4 synthesized at 6 GPa and 450 °C. In addition, we also calculated the bulk moduli according to Errandonea’s method as well as the mode Grüneisen parameters of RCrO4.