We present measurements of internal proper motions at more than five hundred positions of the Eskimo Nebula (NGC 2392), based on images acquired at two epochs with WFPC2 on board the Hubble Space Telescope (the two epochs are separated by 7.695 yr). A detailed comparison of the two observations clearly shows the expansion of the nebula. We measured the amplitude and direction of the motion of local structures in the nebula by determining their relative shift during that interval. In order to assess the potential uncertainties in the determination of proper motions in this object, in general, the measurements were performed using two different methods used previously in the literature. To perform the further scientific analysis we choose the proper motions inferred from the cross-correlation method. By combining our results of the proper motions with radial velocity measurements obtained from high resolution spectroscopic observations, and employing an existing 3D model, we estimate the distance to the nebula to be 1300 pc.