A hybrid construction machine comprising: an internal combustion engine, a hydraulic pump connected to the internal combustion engine, a motor generator connected to the hydraulic pump, a working element (4, 5, 6) driven by the hydraulic pump, a rotation mechanism rotationally driven by a rotation electric motor, a charge storage part connected to an inverter of the motor generator and an inverter of the rotation electric motor, wherein the charge storage part includes a constant voltage charge storage part configured to maintain a voltage value thereof within a certain range, the constant voltage charge storage part including a capacitor between the inverter of the motor generator and the inverter of the rotation electric motor; a variable voltage charge storage part configured to tolerate a variation in a voltage value of the charge storage part due to an electric motor and a generator operation of the motor generator or a power running and a regenerative operation of the rotation electric motor; and a step-up and step-down converter electrically connected between the constant voltage charge storage part and the variable voltage charge storage part to control the charging and discharging of the variable voltage charge storage part. an internal combustion engine, a hydraulic pump connected to the internal combustion engine, a motor generator connected to the hydraulic pump, a working element (4, 5, 6) driven by the hydraulic pump, a rotation mechanism rotationally driven by a rotation electric motor, a charge storage part connected to an inverter of the motor generator and an inverter of the rotation electric motor, wherein the charge storage part includes a constant voltage charge storage part configured to maintain a voltage value thereof within a certain range, the constant voltage charge storage part including a capacitor between the inverter of the motor generator and the inverter of the rotation electric motor; a variable voltage charge storage part configured to tolerate a variation in a voltage value of the charge storage part due to an electric motor and a generator operation of the motor generator or a power running and a regenerative operation of the rotation electric motor; and a step-up and step-down converter electrically connected between the constant voltage charge storage part and the variable voltage charge storage part to control the charging and discharging of the variable voltage charge storage part. a constant voltage charge storage part configured to maintain a voltage value thereof within a certain range, the constant voltage charge storage part including a capacitor between the inverter of the motor generator and the inverter of the rotation electric motor; a variable voltage charge storage part configured to tolerate a variation in a voltage value of the charge storage part due to an electric motor and a generator operation of the motor generator or a power running and a regenerative operation of the rotation electric motor; and a step-up and step-down converter electrically connected between the constant voltage charge storage part and the variable voltage charge storage part to control the charging and discharging of the variable voltage charge storage part.