This paper reports the results of an experimental study to determine the principal thermal conductivities (kx,ky, and kz) of an anisotropic composite medium using an inverse heat transfer analysis. The direct problem consists of solving the three dimensional heat conduction equation in an orthotropic composite medium with the finite difference method to generate the required temperature distribution for known thermal conductivities. The measurement technique involves dissipating a known heat flux at the central region of a square sample and allowing it to conductively transfer the heat to an aluminium cold plate sink via a square copper ring. At steady state, temperatures at 28 (19 are used for retrievals due to symmetry) discrete locations are logged and used for parameter estimation. The entire measurement process is conducted in a vacuum environment. The inverse heat conduction problem (IHCP) for retrieving the orthotropic thermal conductivity tensor(parameter estimation) is then solved using a two layer feed forward back propagation artificial neural network (ANN) trained using the Levenberg–Marquardt algorithm (LMA), with temperatures as input and thermal conductivity values kx,ky, and kz as the output. The method is first validated against a stainless steel(SS-304) sample of known thermal properties followed by the determination of the orthotropic conductivities of the honeycomb composite material.