This research studies the effectiveness of phase change material (PCM) as a thermal insulation for a pipe. The proposed PCM insulation can be used for a pipe when the operating time is limited. The objective of using PCM is to utilize its latent heat from fusion to minimize heat loss from the pipe by absorbing and storing it to be discharged later to the pipe. The finite element method is employed to solve the problem, and both conduction and natural convection of liquid PCM are considered modes of heat transfer. The effectiveness of the PCM insulation is evaluated by comparing its thermal performance with insulation without phase change. Both time-dependent and time-independent boundary conditions are examined. For the time-independent case, the PCM insulation reduces the heat loss from the pipe for a significant amount of time if the Rayleigh number is low. For the time-dependent case, heat loss is eftectively reduced with the PCM insulation for a significant amount of time. The high resolution capturing of the solid/liquid moving boundary and the details of flow structure are also presented.