The effects of high pressure on the crystal structure of orthorhombic (Pnma) perovskite-type cerium scandate were studied in situ under high pressure by means of synchrotron X-ray powder diffraction, using a diamond-anvil cell. We found that the perovskite-type crystal structure remains stable up to 40 GPa, the highest pressure reached in the experiments. The evolution of unit-cell parameters with pressure indicated an anisotropic compression. The room-temperature pressure-volume equation of state (EOS) obtained from the experiments indicated the EOS parameters V0 = 262.5(3) Å3, B0 = 165(7) GPa, and B0' = 6.3(5). From the evolution of microscopic structural parameters like bond distances and coordination polyhedra of cerium and scandium, the macroscopic behavior of CeScO3 under compression was explained and reasoned for its large pressure stability. The reported results are discussed in comparison with high-pressure results from other perovskites.