In an apparatus having a magnetic sensing type metal sensor arranged in spaced relation to a surface of metal under measurement and reciprocable in a predetermined direction, a tracing unit for driving the sensor in accordance with a change in the output of the sensor due to a change of position of the metal in the predetermined direction for causing the sensor to follow the surface position of the metal, and a measuring unit for measuring the surface position of the metal based on a current position of the sensor; a metal surface position measuring apparatus comprising a measuring and storing device for measuring a noise component in the output of the sensor due to factors other than a change of the surface position of the metal and storing the noise component, and correction device for correcting the output of the sensor by the stored noise component and causing the sensor to be moved in accordance with the corrected output.