A boom driving system for a hybrid excavator, comprising: an electric motor which is operated as a motor or a generator; an electric energy storage device which stores electricity produced by the electric motor; a hydraulic pump motor which is operated by the electric motor and supplies a hydraulic fluid to a boom actuator; a boom control valve which configures a closed circuit so as to selectively connect or disconnect a discharge line of the hydraulic pump motor and an inlet line of the hydraulic pump motor to/from a head side or a rod side of a boom cylinder that operates the boom actuator; a first control valve which connects the inlet line to a drain tank; a second control valve which connects the discharge line to the drain tank; and a control unit which controls the electric motor, the hydraulic pump motor, the boom control valve, and the first and second control valves (151, 300), characterized in that the control unit is adapted to control an opening area of the second control valve according to a size of operating torque that is applied to the electric motor when the boom actuator performs a regenerative downward movement or a load downward movement and to determine whether the operating torque that is applied to the electric motor when the boom actuator performs the regenerative downward movement or the load downward movement has a plus (+) value or a minus (-) value, wherein the control unit is adapted to maximally open the second control valve when the minus (-) value of the operating torque indicates that the boom actuator performs the regenerative downward movement, and wherein the control unit is adapted to control the opening area of the second control valve to be reduced when the plus (+) value of the operating torque indicates that the boom actuator performs the load downward movement. an electric motor which is operated as a motor or a generator; an electric energy storage device which stores electricity produced by the electric motor; a hydraulic pump motor which is operated by the electric motor and supplies a hydraulic fluid to a boom actuator; a boom control valve which configures a closed circuit so as to selectively connect or disconnect a discharge line of the hydraulic pump motor and an inlet line of the hydraulic pump motor to/from a head side or a rod side of a boom cylinder that operates the boom actuator; a first control valve which connects the inlet line to a drain tank; a second control valve which connects the discharge line to the drain tank; and a control unit which controls the electric motor, the hydraulic pump motor, the boom control valve, and the first and second control valves (151, 300), characterized in that the control unit is adapted to control an opening area of the second control valve according to a size of operating torque that is applied to the electric motor when the boom actuator performs a regenerative downward movement or a load downward movement and to determine whether the operating torque that is applied to the electric motor when the boom actuator performs the regenerative downward movement or the load downward movement has a plus (+) value or a minus (-) value, wherein the control unit is adapted to maximally open the second control valve when the minus (-) value of the operating torque indicates that the boom actuator performs the regenerative downward movement, and wherein the control unit is adapted to control the opening area of the second control valve to be reduced when the plus (+) value of the operating torque indicates that the boom actuator performs the load downward movement.