The effect of wall axial conduction on the heat transfer in a concentric tube heat exchanger is examined for the inner flow laminar flow regime. The procedure used for the current analysis combines the analytical solution for the inner fluid with a numerical approximation for the wall conduction and has the capability of handling the temperature variation for the outer fluid. Both parallel and counterflow cases are evaluated for the analysis, and results are presented in terms of the axial variations of fluids and wall temperatures. Effects of the heat capacity rate ratio of the fluids on the temperature variations and on the mean heat flux are also pointed out. The effect of the exchanger length is included for the analysis. It is concluded that the total heat transfer between the fluids is greatly influenced by the wall axial conduction for the counterflow arrangement and is not ignorable when the heat capacity rate ratio of fluids are smaller than unity.