A sequential method is proposed to estimate the periodic boundary conditions on the non-Fourier fin problem. An inverse solution is deduced from a finite difference method, the concept of the future time and a modified Newton-Raphson method. Two examples are used to demonstrate the features of the proposed method. The close agreement between the exact values and the estimated results is made to confirm the validity and accuracy of the proposed method. The results show that the proposed method is an accurate and stable method to determine the periodic boundary conditions in the non-Fourier fin problems. (c) 2005 Elsevier Ltd. All rights reserved.