•A thermal conductivity model is developed based on the analogy concept and is applied to pure substances.•Data are included for 24 organic families and 56 functional groups in a temperature range of 16.6 to 604.65 K and pressures below 4032 bar.•The final model presents one interaction parameter that is generalized using the group contribution technique.•Prediction of thermal conductivity in the saturation and single-phase conditions are done.•The model provides acceptable results when in comparison to other correlations. The aim of this work is to apply a group contribution method to describe the thermal conductivity of pure substances. The model has five adjustable parameters that have been generalized using the acentric factor, RTc/Pc relation, and a contribution of each group in the substance through a tendency graphical analysis. The thermodynamical properties included in the model are estimated using a modified Peng-Robinson EoS. The proposed model is applied to 351 substances distributed into 160 for the correlation, 96 for testing, and 95 for predictive capabilities. The above includes 24 organic families and 56 functional groups. The average absolute deviations are below 6.51% for the liquid-vapor coexistence and below 7.93% for the one-phase condition. The overall results are compared to other literature works on saturation and single-phase conditions. These results show that the model provides acceptable values of deviations and can be used to describe different types of substances. Finally, three cases of study are done as an alternative to represent the alkanes, 1-alcohols, and water substances. The average absolute deviations for 1-alkanes and 1-alcohols are below 7.00% and for water is around 3.76%. In general, the generalized model can be used as an alternative to describe the thermal conductivities of pure substances in the saturation and single-phase conditions with acceptable results. A group contribution method to model the thermal conductivity of pure substances. Luis F. Cardona, Luis A. Forero and Jorge A. Velásquez. Display omitted