A numerical formulation based on the singular boundary method (SBM) and the Levenberg-Marquardt (LM) method is presented to determine the thermal conductivity coefficients in 3D anisotropic media. Since all sample points are located on boundary surfaces for the sake of easy access, the SBM is employed to evaluate the direct solution. The unspecified parameters are denoted as the unknown variables in an objective function, which are formulated from the measurements and the calculated results at the boundaries. For the inverse analysis, the LM method is used for minimizing the objective function and obtaining the identified parameters. The results show that the speed of convergence is considerably fast because the number of iterations to approach a satisfied solution is under ten times for single-connected media and twenty times for multiply-connected media. The close agreement between the exact values and the estimated results confirms the validity and accuracy of the proposed strategy. (C) 2016 Elsevier Ltd. All rights reserved.