This study was aimed to improve the SO2 desorption effect of basic aluminum sulfate SO2-rich solution. Based on the desorption mechanism, we first used a falling film evaporation method to intensify heat transfer and mass transfer. Based on the falling film desorption heat and mass transfer model, we analyzed the falling film evaporation and desorption of basic aluminum sulfate SO2-rich solution inside the converging–diverging tube and the smooth tube and investigated the heat and mass transfer rules under different conditions. It was found as the quantity of SO2-rich solution increased, the heat transfer coefficient and mass transfer coefficient of falling film evaporation both increased, but the SO2 desorption efficiency decreased. With the rise of the heating temperature, the three indices all increased. With the rise of the inlet sulfur concentration, the three indices all increased. With the rise of the aluminum concentration, the three indices all gradually declined. With the rise of the alkalinity, the three indices all gradually declined. Comparative analysis showed the heat transfer coefficient and mass transfer coefficient of falling film evaporation and SO2 desorption efficiency were 17%–29%, 33%–69%, and 6.7%–16.3% larger inside the converging–diverging tube than the smooth tube, respectively, indicating the basic aluminum sulfate SO2-rich solution significantly outperforms inside the converging–diverging tube in terms of heat transfer and mass transfer. At the heating temperature of 108 °C, liquid film flow rate of 0.005 kg/s, sulfur concentration of 0.06 mol/L, aluminum concentration of 20 g/L, and basicity of 20%, the SO2 desorption efficiency inside the converging–diverging tube could reach a high level 94.2%, compared with only 83.7% inside the smooth tube. Moreover, correlations were obtained to predict the heat and mass transfer coefficients.