We proposed a reformed mathematical model which can describe the relationship between three inducer inputs and gene expression rate outputs. This model contains 14 biological meaning parameters which can reflect the expression rates under different TF binding states and the features of Hill function curves. We performed two numerical experiments before biological experiments. In order to validate that our model can precisely simulate the real expression data, we used BioBricks from iGEM (International Genetically Engineered Machine) to construct a promoter which contains TFBSs for three kinds of TFs. The proposed mathematical model can fit the real expression data and predict newly generated outputs.