Recently, gamma-ray halos of a few degree extension have been detected around two middle-aged pulsars, namely, Geminga and PSR B0656+14, by the High Altitude Water Cherenkov observatory (HAWC). The gamma-ray radiation arise from relativistic electrons that escape the pulsar wind nebula and diffuse in the surrounding medium. The diffusion coefficient is found to be significantly lower than the average value in the Galactic disk. If so, given a typical transverse velocity of $300-500{\,\rm km /s}$ for a pulsar, the displacement of the pulsars due to the proper motion could be important in shaping the morphology of the pulsar halos. Motivated by this, we study the morphology of pulsar halos considering the proper motion of pulsar. We define three evolutionary phases of pulsar halo to categorize its morphological features. We give the maximum separation angle that can be induced by pulsar proper motion and discuss whether the extended sources observed by HAWC and LHAASO can be associated with pulsar. Generally we do not expect to observe the separation between distant pulsar and halo above 10$\,$TeV with LHAASO or HAWC. Our result can help to interpret the origins of the observed extended sources at very high energies.