1. An apparatus for controlling supercharging pressure in a turbocharger comprising an exhaust turbine and a compressor, said apparatus comprising a variable geometry means at an inlet to said exhaust turbine, an exhaust bypass valve means bypassing said exhaust turbine, an operation detecting means which detects operating conditions of a device connected to receive a supercharging pressure, a supercharging pressure detecting means which detects the supercharging pressure, a deviation calculating means which calculates the deviation of the detected supercharging pressure from a target supercharging pressure to provide a control value based on said deviation, first and second control calculating means which calculate the controlled variable of said variable geometry means and said exhaust bypass valve means in accordance with parameters representative of the operating conditions including said control value, an operating range discriminating means which discriminates in which operating range feedback control is performed and selects whether to perform control in either said variable geometry means or said exhaust bypass valve means in accordance with the result of the operating range discrimination and said control value, and an overboost control means which raises said target supercharging pressure during a predetermined time when sudden acceleration is detected, wherein when said overboost control means is operated for overboost control, the operating range for performing feedback control by said variable geometry means is increased.