Cu2SnS3 is a potential earth-abundant solar material, but its efficiency can differ by orders due to varied growth conditions. A thorough theoretical understanding is necessary. For this purpose, a comprehensive thermodynamic model of the Cu-Sn-S system is constructed under the CALculation of PHAse Diagram (CALPHAD) framework, with the Gibbs energies of solid phases calculated using the first principles phonon method. Good agreements are achieved with extensive experimental data collected systematically, demonstrating high reliability of the model. Then the optimal growth conditions of Cu2SnS3 are studied. We systematically inspect the impacts of Cu/Sn ratio, sulfur content, pressure and temperature, and give reasonable explanations to several experimental observations which are not fully understood before. We find that sufficient sulfur penetration throughout the precursor before annealing is important to obtain desirable morphology and good performance. Combined with kinetic considerations, a detailed synthesis pathway is proposed, with crucial differences compared to a similar one in the literature. The reaction sequence along the pathway is elucidated. The model can also provide guidance to synthesis of the other materials in the Cu-Sn-S system. (C) 2017 Elsevier Ltd. All rights reserved.