The deformation of a non-rigid particle, such as proteins, DNA, and microorganisms, during its electrophoresis can be significant in practice. This effect is simulated by considering the electrophoresis of an ellipsoidal polyelectrolyte (PE) of varying aspect ratios at a fixed volume. We show that both the double-layer polarization and the counterion condensation can be influenced significantly by the shape of an ellipsoidal PE, making its behaviors different both quantitatively and qualitatively from those of a spherical PE. In addition, the electroosmotic retardation flow inside an ellipsoidal PE also plays an important role as its shape varies. The electrophoretic mobility of a PE might have a local maximum as the amount of its fixed charge varies, which is consistent with the experimental observations in the literature. The level of the amount of the fixed charge at which the local maximum in the electrophoretic mobility occurs depends upon the PE shape, which has not been reported in previous theoretical studies. The results gathered in this study provide valuable information for both the interpretation of experimental observation and the design of relevant electrophoresis devices.