Provided is an engine-exhaust-gas energy recovery apparatus including a hybrid turbocharger having a turbine unit that is supplied with exhaust gas discharged from an engine, a compressor unit that pressure-feeds scavenging-air pressure to the engine, and a generator/motor unit that generates electricity when the turbine unit is driven; a bypass channel that allows the exhaust gas supplied toward the hybrid turbocharger to bypass the hybrid turbocharger; an engine-load detecting part; an engine-rotation-speed detecting part; a scavenging-air-pressure detecting part; and a control device having a database for calculating a scavenging-air pressure, at which the fuel consumption rate of the engine becomes lower than or equal to a predetermined value, from the detection values of the respective detecting parts. The control device controls an exhaust-gas bypass control valve so as to control the scavenging-air pressure of the engine.