A stepper motor is accelerated and decelerated with a parabolic velocity profile to efficiently utilize the available torque of the motor. The times between pulses to obtain a parabolic velocity profile are determined by a microprocessor-based stepper motor controller from desired values of start/stop velocity, maximum velocity and time to reach maximum velocity. The required times are stored in a random access memory and are used to supply to the motor a pulse train which follows the parabolic velocity profile during acceleration and deceleration. The controller is easily programmable to accommodate different motor characteristics, different applications and different operating parameters.