For the electro-discharge machining of an electro-conductive anisotropic composite, an unsteady state formulation was established and solved by Galerkin‘s finite element method. The distribution of temperature on work piece, the shape of the crater and the material removal rate were obtained in terms of the process parameters. The 12×12 irregular mesh that was chosen as the optimum in the previous analysis was used for computational accuracy and efficiency. A material having the physical properties of alumina/titanium carbide composite was selected and an electricity with power of 51.4 V and current of 7 A was applied, assuming the removal efficiency of 10 % and the thermal anisotropic factors of 2 and 3. As the spark was initiated the workpiece immediately started to melt and the heat affected zone was formed. The moving boundary of the crater was also identified with time. When the radial and axial conductivities were increased separately, the temperature distribution and the shape of the crater were shifted in the radial and axial directions, respectively. The material removal rate was found to be higher when the conductivity was increased in the radial direction rather than in the axial direction.