A new numerical method-nodal green's function method is used for solving heat conduction function. A heat conduction problem in cylindrical geometry with axial conduction is solving in this paper.The Kirchhoff transformation is used to deal with the problem with temperature dependent conductivity. There for the calculation for the function is simplified. On the basis of the formulas developed, the code named NGMEFC is programmed. A sample problem which has been calculated by the code GOBRA-Ⅳ is chosen as the check problem. A good agreement is achieved between both codes.The calculation shows that the calculation efficiency of the nodel green's function method is much higher than that of finite difference method.