This paper reports a methodology to estimate the principal thermal conductivities (kx and ky) of an orthotropic composite material by using inverse heat transfer. In the study a two dimensional steady state heat conduction equation with heat generation for an orthotropic material has been investigated. A grid independent study has been carried out using ANSYS for fine mesh size and its obtained as 120x120.With this mesh size of 120x120 by varying the thermal conductivities the temperature distribution of the orthotropic composite material at different location are calculated and these values are used for inverse heat transfer analysis using Artificial neural network(ANN).