Color-tunable luminescence in phosphors can be achieved in a number of ways. In this study, a series of Ce3+/Tb3+ singly doped and (Ce3+,Tb3+) doubly doped Sr5(BO3)3F (SBOF) phosphors, having color point tuning properties, were synthesized by solid-state reaction. The emission color can be adjustable in two ways: by means of changing Ce3+ concentration or doubly doping Ce3+ and Tb3+ ions. The variation in the Ce3+ concentration in Ce3+ singly doped SBOF shows a red shift of the emission. The red shift can be assigned to energy transfer between Ce3+ ions at different sites. In the SBOF:Ce3+,Tb3+ samples, adjustable emission from blue to green can also be obtained by changing Tb3+ doping concentration when Ce3+ content is fixed under UV excitation. This is due to the energy transfer process from Ce3+ to Tb3+ in SBOF:Ce3+,Tb3+ phosphors. Moreover, the characteristic emission peak intensity of Tb3+ in the co-doped sample is enhanced by about 40 times compared with the single-doped Tb3+ phosphor under near-ultraviolet excitation. The potential application of this green-emitting phosphor in UV chip excited white LED was evaluated.