In the galaxy, extremely large mass-ratio inspirals (X-MRIs) composed of brown dwarfs and the massive black hole at the galactic center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty X-MRI systems by an axisymmetric Konoplya–Rezzolla–Zhidenko metric with varied parameters. We find that the mass, spin, and deviation parameters of the Kerr black hole can be determined accurately (∼10−5−10−6) with only one X-MRI event with a high signal-to-noise ratio. The measurement of the above parameters could be improved with more X-MRI observations.