This research investigates the thermal characteristics of a thermal insulation for a pipe with a phase change material (PCM) for an unsteady operating condition. A layer of the PCM located at the inner surface of the insulation is aimed to minimize the heat loss from the pipe by absorbing and storing the heat loss in the form of latent and sensible heats. A convection boundary condition is applied at the inner and outer surfaces of the insulation, and one-dimensional finite element method is utilized to solve the problem. The effectiveness of the insulation with the PCM is evaluated by comparing the heat loss to insulation without a PCM. The effect of the PCM type, the PCM layer thickness, and temperature cycle of the inner surface is studied. The results indicate that heat loss is reduced significantly when the PCM layer is used for a significant amount of time, and the heat loss is reduced more when the quantity of the PCM is increased. The temperature cycle has an insignificant influence on the thermal performance of the insulation with the PCM.