We investigated the energy transfer among three rare-earth ions, Ce3+, Tb3+, and Eu3+, and the related emission properties in a host material CaHfO3 by using photoluminescence spectroscopy. We found that in case of the Tb3+ and Eu3+ doubly-doped CaHfO3, the visible emission intensity of Eu3+ could be activated with the photoexcitation of the transitions in Tb3+ through an energy transfer from Tb3+ to Eu3+. By adding Ce3+ ions to this doubly doped sample, we obtained the Eu3+ emission with near-ultraviolet (NUV) light excitation in Ce3+ via the successive energy transfers Ce3+ → Tb3+ and Tb3+ → Eu3+. We observed that the emission colors were tuned from blue to green/yellow and then to red with NUV photoexcitation in Ce3+/Tb3+/Eu3+-codoped CaHfO3.