The exact method with small time-lag of detecting screw back pressure for controlling the screw back pressure in the plasticizing process of an electric-motor driven injection molding machine without using a pressure detector has been asked for because the pressure detector is very expensive, necessitates troublesome works for mounting, an electric protection against noise and the works for zero-point and span adjustings and causes a complicate mechanical structure.The present invention uses a high-gain observer which contains the discrete-time arithmetic expressions derived from a mathematical model of a plasticizing mechanism in an electric-motor driven injection molding machine consisting of state equations and outputs an estimate of screw back pressure, which is one of the state variables of the above state equations, by using a screw position signal, a servomotor current demand signal or actual motor current signal and a screw revolution speed signal as inputs. The high-gain observer obtains the exact screw back pressure estimate with very small time-lag without using a pressure detector. Thus the estimate of screw back pressure fed by the high-gain observer can be adopted as a feedback signal of actual screw back pressure for controlling the screw back pressure in the plasticizing process.