A method for steady-state thermal conductivity measurement with single constant temperature region has been developed. To better understand the accuracy of the method a numerical model is devised and verified by experimental results. The ratios of thermal conductivity derived from the temperature distribution solutions to that given in the numerical model are obtained and shown. They can be used to correct the systematic error of measurement introduced by the one-dimensional approximation. Finally, the measurement uncertainty due to misalignment of the temperature sensors and the limitation of sensing devices is also investigated. The numerical model is suitable for estimating the range of confidence in practical measurements.