[Problem] An object of the present invention is to provide an electric power steering apparatus that constitutes a control system based on a physical model, constitutes a model following control that an output (a distance to a rack end) of a controlled object follows-up to a reference model, suppresses the occurrences of a noisy sound and a shock force at an end hitting without giving any uncomfortable steering feeling to a driver, and is capable of smoothly steering.[Means for solving the problem]In the 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 the first current command value, the apparatus comprises a configuration of a model following control comprising a feed-back control section including a viscoelastic model as a reference model within a predetermined angle at front of a rack end, wherein the configuration of the model following control comprises a feed-back control section, and the model following control has a noise-reducing function to reduce a noise so as to suppress a rack end hitting.