In a motor-driven power steering apparatus for converting rotation of an electric motor into a linear stroke of a rack shaft by an interposition of a power transmission mechanism and steering a tire wheel connected to the rack shaft, there is provided a motor slip detecting means for previously determining a cumulative rotational speed of the electric motor corresponding to a maximum stroke displacement amount of the rack shaft, integrating the rotational speed of the electric motor, and estimating that slip or idle running is generated in a rotational force transmission system from the electric motor to the rack shaft, where the integral rotational speed of the electric motor becomes more than a prescribed cumulative rotational speed.