The mathematical model based on graph theory and the refrigerant natural cycle system of gas-liquid two-phase flow network is established. Incidence matrix was used to describe the relationships between the various components. The node conservation equations, branch equations, momentum conservation equation in return circuit and mass conservation equations of system are established. The model was solved by using variable step gird iterative method. Then refrigerant state of each node and refrigerant flow of each branch in network model are obtained. Establishment and solution of the RNC network model provides an effective way for the further performance analysis of system.