1. An apparatus for controlling pressure in an electric-motor driven injection molding machine having an injection and pressure application mechanism in which rotation of a servomotor is transferred to rotation of a ball screw through a reduction gear and rotation of said ball screw is converted to a linear motion of a nut of said ball screw and said nut drives a moving part and a linear motion of a screw is realized through said moving part and pressure application to a melted polymer stored at the end of a barrel and fill-up of a cavity with polymer melt are realized by a movement of said screw, comprising: an injection controller operative to provide a motor current demand signal for said servomotor to external, which comprises a high-gain observer operative to execute at a constant time interval discrete-time arithmetic expressions derived by applying a standard method of forward rectangular rule to a continuous-time mathematical model of an injection mechanism representing motion equations of said injection and pressure application mechanism and consisting of state equations having two state variables of an injection velocity variable and an injection pressure variable and having two input variables of said motor current demand signal applied to said servomotor or actual motor current signal and a screw position signal and an output equation having one output variable of an injection velocity signal as a measurable state variable and operative to execute at a constant time interval a discrete-time expression of time integration derived by applying a standard method of trapezoid rule to a continuous-time time integration equation between a screw position and an injection velocity, an injection pressure setting device operative to feed an injection pressure command signal, a subtracter operative to feed a difference signal between said injection pressure command signal from said injection pressure setting device and an estimate of injection pressure which said high-gain observer outputs by using an injection velocity signal detected by a rotary encoder mounted on said servomotor axis and a differentiator and said motor current demand signal applied to said servomotor or said actual servomotor current signal as inputs and by executing said discrete-time arithmetic expressions and said discrete-time expression of time integration built in, and a pressure controller operative to derive said motor current demand signal for said servomotor by using said difference signal from said subtracter so that said estimate of injection pressure follows said injection pressure command signal; and a motor controller fed said motor current demand signal from said injection controller.