Disclosed is a speed controlling method and apparatus in which a suitable current or voltage command is given to a moving body on the basis of the relation between a speed detection signal obtained by detecting the speed of the moving body and an externally supplied speed command signal. The speed of the moving body is controlled in a manner so that the speed of the moving body is successively detected, a speed error which is a difference between a speed command value and a speed detection value is calculated whenever the speed of the moving body is detected, and the speed of the moving body is successively controlled on the basis of a driving signal obtained by an arithmetic operation on the basis of the speed error and a set control gain, and that, on the other hand, a present speed error quantity is calculated on the basis of speed errors obtained whenever the detection of the speed of the moving body have been carried out predetermined number of times, the speed error quantity obtained presently is compared with and the speed error quantity obtained last, and the set gain is corrected or updated in accordance with the result of comparison of the present and last speed error quantities to thereby minimize the speed error quantity.