A motor speed control method and system allow the motor to be accelerated to the steady state in the minimum time even under conditions of varying load torque, varying load inertia and varying power voltage. The motor is controlled by a voltage including a component of proportional term which is a function of a difference between a command speed and a detected speed, and a component of integral term which is summed during an acceleration phase. The acceleration of the motor during the starting process is measured and the integral term is modified basing on the result. The integral term may be memorized so that it is used as the integral term when the subsequent starting phase is completed. The integral term may be obtained from the acceleration and deceleration in the starting process.