An analytical method has been developed for the inverse heat conduction problem, when the temperatures are known at two positions in a finite body or at one position in a semi-infinite body. On the basis of these known temperatures, a closed form solution is determined for the transient temperatures beyond the two positions by using Laplace transform technique. This method first approximates the temperature data with a half polynomial power series of time. The resultant expression for an objective temperature or heat flux is explicitly obtained in the form of power series of time. Numerical results for some representative problems show that the surface temperature and heat flux can be predicted well by the method.