The effects of high pressure on the crystal structure of orthorhombic (Pnma) perovskite type cerium scandate have been studied in situ under high pressure by means of synchrotron x-ray powder diffraction, using a diamond anvil cell. We have 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 has indicated an anisotropic compression. The room-temperature pressure-volume equation of state is obtained from the experiments. From the evolution of microscopic structural parameters like bond distances and coordination polyhedra of cerium and scandium, the macroscopic behavior of CeScO3 under compression has been explained and reasoned for its large pressure stability. The reported results are discussed in comparison with high-pressure results from other perovskites.