An electric power steering apparatus includes a temperature sensor measuring a temperature at a starting of a vehicle, a motor position sensor detecting a relative steering angle of a motor, a cumulative transfer calculation unit calculating a cumulative transfer quantity of a rack bar by information detected in the motor position sensor, a counter calculating an elapsed time from a starting time of the vehicle, a friction coefficient determination unit determining a friction coefficient according to information inputted from the temperature sensor, the cumulative transfer quantity calculation unit, and the counter, respectively, by using a setting map of a friction coefficient, and a target current calculation unit calculating a compensation quantity for a friction by using the friction coefficient determined in the friction coefficient determination unit and determining a target current.