Radiation displacement effect of BaTiO3 ferroelectric under epitaxial compressive strain is studied by using molecular dynamics simulations which is based on shell model. The numbers of defects, distributions and changes of polarization in the system are calculated before and after radiation under epitaxial compressive strains of 0, 0.4%, 0.8%, 1.2%, 1.6%, 2.0% respectively by using O atom of 1 keV and [001] direction as a primary konck-on atom (PKA). The damaged areas, the displacement distances of the defect, and migration distances of PKA under reverse applied electric field, obtained in the two cases: 2% compressive strain and no strain, are compared. The results show that the polarization of system increases almost linearly with increasing the epitaxial compressive strain, and that both the polarization amplitude and the number of defects decrease after irradiation. The displacement distance of defects under 2% compressive strain, migration distance of PKA under reverse applied electrical field and damaged area are all smaller than under no strain condition, which indicates that epitaxial compressive strain can suppress lattice irradiation damage, and the damage in BaTiO3 can be tuned by introducing epitaxial compressive strain.