Heat transfer by laminar oscillating flow in a circular pipe has been studied analytically. The general solution with respect to the arbitrary wall boundary condition is obtained by superposing the fluid temperatures with the sinusoidal wall temperature distributions. The fulid temperature distributions are two dimensional, but uniform flow assumption is used to simplify the velocity distribution. The heat transfer characteristics in the thermally developing regions are analyzed by applying the general solution to the two cases of thermal boundary conditions in which the wall temperature and wall heat flux distributions have a square-wave form, respectively. The results show that the length of the thermally developing region becomes larger in proportion to the oscillation frequency at slow oscillation and eventually approaches to the value comparable to the swept distance as the frequency increases. The time and cross-section averaged Nusselt number in the developing region is inversely proportional to the square root of the distance from the position where the wall boundary condition is changed suddenly. In the developed region, Nusselt number is only determined by the oscillation frequency.