A solution scheme based on the maximum entropy method (MEM) for the solution of one-dimensional inverse heat conduction problem is proposed. The present work introduces MEM in order to build a robust formulation of the inverse problem. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. In order to seek the most likely inverse solution, the present method converts the inverse problem to a non-linear constrained optimization problem. The constraint of the problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the maximum entropy estimation. The characteristic feature of the method is discussed with the sample numerical results. The presented results show considerable enhancement in the resolution of the inverse problem and bias reduction in comparison with the conventional methods.