Tb³⁺ is a typical green emitting luminescence center in inorganic compounds. However, the absorption of Tb³⁺ is very weak in ultraviolet spectral region (from 240 to 400 nm). Ce³⁺ is often used as a sensitizer to transfer energy to Tb³⁺. In this paper, Ce³⁺ and Tb³⁺ were co-doped into a novel aluminates-borates LaAl_2.03B₄O_10.54. Ce³⁺ can absorb UV light (from 240 to 340 nm) and transfer absorbed energy to co-doped Tb³⁺ effectively and bring bright green emission of Tb³⁺. The crystal structure and fluorescence spectra of phosphors, the efficiency of energy transfer between Ce³⁺ and Tb³⁺, decay dynamics, the thermal stability and internal quantum efficiency of luminescence have been investigated in detail. These results indicate that the color tunable LaAl_2.03B₄O_10.54: Ce³⁺, Tb³⁺ phosphor is a potential green-emitting material. Especially, analysis about the relationship of the doping concentration of luminescence centers and thermal stability of luminescence points out a feasible way to enhance the thermal stability of luminescence in the future.