In an electric power steering apparatus for a motor vehicle comprising a rack shaft (1) provided with first and second rack portions (14 and 15), a pinion (21) of a steering shaft for meshing with the first rack portion (14), and a pinion (31) of an electric motor (34) for meshing with the second rack portion (15), the first rack portion (14) is constructed to have a constant gear ratio and the second rack portion (15) is constructed to have a variable ratio so that an abnormal feeling during a steering operation is prevented and the lock to lock of a steering wheel is reduced to a small value.