In order to obtain the Er³⁺/Yb³⁺ co-doped Ba₅Gd₈Zn₄O₂₁ up-conversion phosphor material with maximum red luminous intensity, three steps are adopted as follows. Firstly, the uniform design in the experimental optimal design is used to find the reasonable doping concentration of Er³⁺/Yb³⁺. Secondly, according to the quadratic general rotary unitized design, the regression equation of the red luminescence intensity of Er³⁺/Yb³⁺ co-doped Ba₅Gd₈Zn₄O₂₁ under 980 nm and 1550 nm excitations is established. Finally, the optimal solution of the regression equation is obtained by genetic algorithm. The Ba₅Gd₈Zn₄O₂₁:Er³⁺/Yb³⁺ phosphors are prepared by a high-temperature solid-phase method. The crystal structure for each of the prepared phosphors is analyzed by X-ray diffraction, and it is confirmed that the prepared phosphor samples of Ba₅Gd₈Zn₄O₂₁ are all in pure phase. Using the 980 nm laser as an excitation source, the relationship between the red up-conversion luminescence intensity of the optimal sample and the operating current of the laser is studied. It is found that the red luminescence is emitted through a double-photon process by the formula fitting analysis. Using the 1550 nm laser as the excitation source, it is found that red luminescence is emitted through a three-photon process. The up-conversion emission spectrum of the optimal sample with respect to temperature is measured and discussed, and it is found that the red up-conversion luminescence intensity of the sample is weakened as the temperature increases. The optimal samples are compared with the commercial phosphors of NaYF₄:Er³⁺/Yb³⁺ under the 980 nm and 1550 nm excitation respectively, the luminescence intensity of the optimal sample is much stronger than that of the commercial phosphor of NaYF₄:Er³⁺/Yb³⁺. Moreover, under the same power density excitation, the red up conversion luminescence intensity of the optimal sample at 980 nm is stronger than that at 1550 nm.