A fast numerical method that combines the finite element and finite difference methods (FE-FDM) is proposed to analyze the forced convection heat transfer performance of graded honeycomb heat exchangers. The temperature distribution in the cross-section of the graded honeycomb perpendicular to the direction of flow is described using discrete finite elements that include the convective heat transfer of the two side surfaces. The temperature distribution in the flow direction is obtained by the finite different method. The most important difference with previous methods is the assumption of Constant Cross-sectional Fluid Temperature (CCFT) is relaxed. The fluid temperature of every individual channel is assumed constant and the different channels may have different temperatures in the same cross-section. Comparison with the results by the CFD model shows that FE-FDM has high precision and efficiency. The results of examples illustrate that its precision is similar to CFD model, but its calculation efficiency is increased 10(2)-10(4) times as compared to CFD simulation. The assumption of CCFT is only suitable for heat transfer analysis of uniform honeycombs. (C) 2014 Elsevier Ltd. All rights reserved.