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We report a large enhancement of spin-torque diode sensitivity in CoFeB/MgO/CoFeB magnetic tunnel junctions measured under perpendicular magnetic fields and dc bias currents. In the measurement of homodyne detection, a large dc output voltage of 190 μV was obtained when an RF signal power of -30 dB ·m and a dc current of +1.0 mA were applied. This value corresponds to the diode sensitivity of 190 mV/mW (260 mV/mW after impedance matching correction). The main origin of this enhancement is an offset of the damping torque and an increase in the precession angle induced by the spin-transfer torque due to the dc bias current application.