A new Group Contribution Method based on elements and chemical bonds was proposed to predict the enthalpy of evaporation of organic compounds at their normal boiling points. A prediction model was built using 1266 experimental data points, and the accuracy of the model estimations was evaluated using 16 experimental data points. The new method has only 42 groups, a simple way of group splitting, and a wide range of predictions with an average relative error of 5.84%. Furthermore, the inclusion of silicon elements and their chemical bonds in the group library enables the effective prediction of silicon-containing compounds with an average relative error of 2.71%. By analyzing and comparing the other three commonly used methods, it can be concluded that the new method provides accurate and reliable estimation results and has a more comprehensive application range.