Systematic analysis of leaf area index variation characteristics is the basis for constructing a model for practical application of crop growth. The meteorological data and crop leaf area index change data were collected and used for analytical modeling. Based on the analysis of the parameters of existing leaf area index model and the relative growing degree days as the independent variable, the modified Logistic model was used to analyze the growth characteristics of the relative leaf area index of winter wheat, summer maize and rice, and the relationship among the model parameters were established. The results showed that the parameters a, b and c were related to the relative growing degree days eigenvalues. With the increase of c, the value of a was increased and that of b was decreased gradually, and its increase or decrease rate was related to the relative growing degree days, and the rate of change of the three crops was different. At the same time, there was a certain functional relationship between parameters a, c and b. Based on the relationship between parameters, the Logistic model of relative modification was simplified, and a single parameter Logistic model describing the leaf area index growth process of three crops of winter wheat, summer maize and rice was established. The model was evaluated using measured data. The results showed that the single parameter model can simulate the growth process of the relative leaf area index. The simplified model had the characteristics of less parameters, simple form and convenient analysis, so it was easy to popularize and apply, and had certain reference value for establishing single parameter relative leaf area index model of other crops.