Discrete and small samples data are usually obtained from the studies on photocatalytic removal of pollutants in water. The first-order kinetic model used to simulate and analyze the experimental data sometimes has poor fitting effect and cannot be used for data prediction. In this study, based on the discrete grey model (DGM(1, 1)), the nonlinear dynamic discrete gray model (EDGM(1, 1, α)) are established by considering the nonlinear characteristics of the data and equal dimensional information substitution method. The model is used to predict the experimental data of photocatalytic degradation of tetracycline by Bi/BiOCl/Au. As compared with DGM(1, 1) and other three models, the EDGM(1, 1, α) model has a better prediction level for the experimental data of photocatalysis. The results are in good agreement with the experimental results. This model can be used to guide the next step of experiments, which is expected to reduce the number of experiments and realize the rapid development of experimental research with low cost and energy consumption.