An electric power steering apparatus that calculates a first current command value based on at least a steering torque and performs an assist-control of a steering system by driving a motor based on said first current command value, characterized in that said electric power steering apparatus comprises: a first converting section to convert said first current command value to a first rack axial force; a rack position converting section to converting a rotational angle of said motor to a judgment rack position; a rack end approach judging section to judge that a steering approaches to a rack end based on said judgment rack position and to output a rack displacement and a switching signal; a viscoelastic model following control section to generate a second rack axial force including a viscoelastic model as a reference model based on said first rack axial force, said rack displacement and said switching signal; and a second converting section to convert said second rack axial force to a second current command value; wherein said viscoelastic model following control section comprising: a feed-forward control section to feed-forward control based on said first rack axial force and to output a third rack axial force; a feed-back control section to feed-back control based on said rack displacement and said first rack axial force and to output a fourth rack axial force; a first switching section to switch-ON/OFF an output of said third rack axial force by said switching signal; a second switching section to switch-ON/OFF an output of said fourth rack axial force by said switching signal; and an adding section to output said second rack axial force by adding outputs of said first and second switching sections; wherein said assist-control is performed by adding said second current command value to said first current command value so as to suppress a rack end hitting. a first converting section to convert said first current command value to a first rack axial force; a rack position converting section to converting a rotational angle of said motor to a judgment rack position; a rack end approach judging section to judge that a steering approaches to a rack end based on said judgment rack position and to output a rack displacement and a switching signal; a viscoelastic model following control section to generate a second rack axial force including a viscoelastic model as a reference model based on said first rack axial force, said rack displacement and said switching signal; and a second converting section to convert said second rack axial force to a second current command value; wherein said viscoelastic model following control section comprising: a feed-forward control section to feed-forward control based on said first rack axial force and to output a third rack axial force; a feed-back control section to feed-back control based on said rack displacement and said first rack axial force and to output a fourth rack axial force; a first switching section to switch-ON/OFF an output of said third rack axial force by said switching signal; a second switching section to switch-ON/OFF an output of said fourth rack axial force by said switching signal; and an adding section to output said second rack axial force by adding outputs of said first and second switching sections; a feed-forward control section to feed-forward control based on said first rack axial force and to output a third rack axial force; a feed-back control section to feed-back control based on said rack displacement and said first rack axial force and to output a fourth rack axial force; a first switching section to switch-ON/OFF an output of said third rack axial force by said switching signal; a second switching section to switch-ON/OFF an output of said fourth rack axial force by said switching signal; and an adding section to output said second rack axial force by adding outputs of said first and second switching sections; wherein said assist-control is performed by adding said second current command value to said first current command value so as to suppress a rack end hitting.