A novel interferometric fiber-optic gyroscope with amplified optical feedback by an Er-doped fiber amplifier (EDFA) is proposed and theoretically investigated (the proposed gyroscope is named the feedback EDFA-FOG, FE-FOG in what follows). The FE-FOG functions like a resonant fiber-optic gyro (R-FOG) because of its multiple utilization of the Sagnac loop; however, it is completely different because a low-coherence light source is used. In addition, the gyro output signal is pulsed because the modulation frequency of the phase modulator placed in the Sagnac loop is selected to match the total round-trip time delay of the light, which includes the Sagnac-loop delay plus that of the feedback loop of the fiber amplifier. The sharpness of the output pulse can be adjusted by both the gain of an EDFA and the modulation depth of the phase modulator. When rotation occurs the peak position of the output pulse is shifted as a result of the Sagnac effect. The resolution of the rotation measurement depends on the sharpness of the output pulse. The techniques of both the open-loop and closed-loop methods are described in detail, which shows the great advantage of the proposed gyroscope over the to the conventional interferometric fiber-optical gyroscope (I-FOG).