We studied the electrophoresis of polyelectrolyte chains, such as DNA, in linear polymer solutions using Brownian dynamics simulation with anisotropic friction tensor. We show anisotropic friction is an effective method to describe dynamics of polyelectrolyte chains under an electric field in dilute polymer solution as well as in entangled polymer solution or gel. With a low anisotropy of friction, a chain fluctuates between elongated and compact states with no periodicity under a steady electric field and in field-inversion electrophoresis, its mobility shows an abrupt change at a certain chain length without antiresonance. With a high anisotropy of friction, a chain oscillates periodically and in field-inversion electrophoresis its mobility shows antiresonance. The above results agree well with experiments on DNA electrophoresis.