In the paper, we have successfully prepared hexagonal boron nitride (h-BN) phosphors with melamine as the nitrogen source. The X-ray powder diffraction patterns confirm that the sample possesses a hexagonal crystal structure within the Pm2 space group. It is interesting that the co-doping combination of Tb3+ and Ce3+ can markedly enhance the threshold concentration of doped activators within the limited solid solution of h-BN phosphors. Under 302 nm excitation, the h-BN:Ce3+ phosphors exhibit broadband blue light emission at 406 nm. In h-BN:Tb3+, Ce3+ phosphors, the co-doping of Ce3+ not only ensures high phase purity but also results in strong green light emission. The energy transfer efficiency from Ce3+ to Tb3+ is about 55%. The fluorescence lifetime increases with the increase of Ce3+ and Tb3+ concentration, and the fluorescence lifetime of h-BN:0.025Tb3+, 0.05Ce3+ phosphor reached 2.087 ms. Additionally, the h-BN:0.025Tb3+, 0.05Ce3+ phosphor exhibits excellent thermal performance with an activation energy value of 0.2825 eV. Moreover, the photoluminescence quantum yield of the sample exceeds 52%. Therefore, the h-BN:Tb3+, Ce3+ samples can be used as green phosphors for solid state lighting and fluorescent labeling.