A steering handle neutral position estimating apparatus for use with a motor vehicle having a steering handle operable to provide a driver's vehicle steering demand. The apparatus comprises a first sensor sensitive to steering handle position for producing an electric signal indicative of a sensed steering handle position, and a second sensor sensitive to steering handle position for producing a steering handle neutral position signal having a first level when the sensed steering handle position is in a predetermined range and a second level when the sensed steering handle is out of the predetermined range. The first and second sensors are coupled to an estimating unit which estimates a sterring handle neutral position when four conditions are fulfilled; that is when the steering handle neutral position signal is at its first level, when the steering handle position change is less than a reference value, when the vehicle continuous traveling distance is greater than a reference value, and the vehicle traveling speed is greater than a first reference value and less than a second, greater reference value.