Establishing a strength model for cement-stabilized clayey soils is crucial to the design and construction of cement-reinforced foundation projects. Numerous studies have used the parameters to establish the strength model, but the selection of the key characterization parameters that determine the strength development remains challenging. Therefore, more studies and indoor tests are required to verify the parameters. This study designs cement-stabilized pure clay particles (i.e., kaolin) with various characterization parameters and conducts a series of unconfined compressive strength tests. Using the results from the strength tests to clarify the influence mechanism for the characterization parameters, the strongly correlated characterization parameters were identified with correlation analysis, and these parameters were used to establish a multilinear regression model for strength. The experimental results showed that Pearson's correlation analysis could effectively identify the relationship between the characterization parameters of the soil particles, water, and cement, and the strength of cement-stabilized clayey soils at different curing times and their correlation intensity. The multilinear regression-based strength model was determined based on a strong Pearson's correlation. The predicted value is similar to the measured value, with a correlation coefficient of 0.985, a mean absolute error (MAE) of 163.80 kPa, and the predicted root mean square error (RMSE) of 225.99 kPa. This study's findings could provide theoretical support for the strength design and performance prediction of cement-stabilized clayey soils.