In order to obtain the Er3+/Yb3+ co-doped BaGd2ZnO5 up-conversion phosphor which has the maximum green and red emission intensity, firstly, the method of homogeneous design rooted in the experimental optimal design is employed to search optimum Er3+/Yb3+doping concentration preliminarily. Next, the quadratic general rotary unitized design is adopted to further optimize the experiment, and the regression equation in green and red emission intensity is established as a function of the doping concentration of Er3+/Yb3+. Finally, the optimal solution, that is, the doping concentration of Er3+/Yb3+ corresponding to the maximum emission intensity, is calculated by genetic algorithm. The optimal Er3+/Yb3+co-doped BaGd2ZnO5 phosphor is synthesized by the conventional high temperature solid state method. The crystal structure of as-prepared products is characterized by X-ray diffraction (XRD), and the results show that all the Er3+/Yb3+co-doped BaGd2ZnO5 phosphors we synthesized are of pure phase. The steady-state up-conversion (UC) emission spectra of products are measured under the excitation of a continuous 980 nm laser diode at different working currents. From the UC luminescent spectra of Er3+/Yb3+co-doped BaGd2ZnO5 phosphor, we can see a red emission centered at 662 nm, two green emissions centered at 551 nm and 527 nm, which are assigned to 4F9/2→4I15/2, 4S3/2→4I15/2 and 2H11/2→$4I15/2 transitions of Er3+ ion, respectively. The dependences of green and red UC emission intensities of optimal samples on working current are investigated, indicating that the red emission and green emission of optimal samples both originate from two-photon process. From the normalized green UC emission spectra, it can be concluded that the experimental laser working current induced temperature variation of samples can be omitted. According to Boltzmann distribution law and the thermal equilibrium existing between the levels of 2H11/2 and 4S3/2, the relationship between green emission and temperature in the optimal green UC emission sample is discussed in depth, and the energy level gap between 2H11/2 level and 4S3/2 level is calculated to be 926.11 cm-1. Through the study of the temperature effect on the optimal green UC emission sample, we find that the emission intensity decreases with the increasing of the temperature, owing to the thermal quenching effect. Furthermore, we calculate the activation energies of the samples, the activation energies of the green emission, red emission, and the overall emission are deduced to be 0.45, 0.46, and 0.45 eV, respectively.