The octupole deformation of even-even Raisotopes has been investigated systematically by the reflection asymmetric relativistic mean field (RAS-RMF) theory. The results are compared with the experimental data together with the results from FRDM. It is shown that RAS-RMF theory gives a good description for Ra isotopes. The calculated binding energy, two neutron separation energy and deformation agree with the experimental data well. In particular, RAS-RMF theory provides the neutron and proton densities which show clearly the shape evolution of these nuclei from nearly spherical to well-developed octupole and finally back to quadrupole deformation shapes. This is in accordance with experimental observation.