High-precision interferometers play a critical role in the field of metrology. The uncertainty of phase estimation can be used to evaluate the precision of an interferometer. The lower the uncertainty of phase estimation, the higher the phase sensitivity. We theoretically propose a nonlinear interferometer composed of an optical parametric amplifier and a linear optical beam splitter (BS). An optical parametric amplifier based on the hot rubidium-85 atomic ensemble four-wave mixing (FWM) process is used to combine and separate the beams in the interferometer. As a feedback controller, the BS controls the proportion of the output light returning to the input light port in the FWM process by controlling the reflectivity of the device. Through theoretical calculations, it is proved that the phase sensitivity of a nonlinear interferometer based on optical parametric amplifier feedback is enhanced compared with that of traditional interferometers. Our research results are expected to have potential applications in the field of quantum metrology.