A low cost crank operated injection apparatus is capable of driving an injection screw with a desired driving force without the need of employing a high output type electric motor. The injection apparatus includes a crank mechanism for converting forward and reverse rotation of a driving shaft into reciprocating motion of an injection screw mounted on a pusher plate. The driving shaft is coupled through a reduction gearing unit to the power output shaft of a servomotor controlled by a numerical control device, and the apparatus operates, during the injection process, so as to cause the injection screw to move forwardly with a great driving force. The servomotor is rotated in such a manner that the driving shaft is driven forwardly within a predetermined rotary angular region corresponding to an operational region which does not include the dead center positions of the crank mechanism, whereby rapid changes in the injection speed and in the rate of change of injection pressure are eliminated during the operating cycle.