We present results from a deep (174 ks) Chandra observation of the FR-II radio galaxy 3C 220.1, the central brightest cluster galaxy (BCG) of a kT ∼ 4 keV cluster at z = 0.61. The temperature of the hot cluster medium drops from ∼5.9 to ∼3.9 keV at ∼35 kpc radius, while the temperature at smaller radii may be substantially lower. The central active galactic nucleus (AGN) outshines thewhole cluster in X-rays,with a bolometric luminosity of 2.0×1046 erg s-1 (∼10 per cent of the Eddington rate). The system shows a pair of potential X-ray cavities ∼35 kpc east and west of the nucleus. The cavity power is estimated within the range of 1.0 × 1044 and 1.7 × 1045 erg s-1, from different methods. The X-ray enhancements in the radio lobes could be due to inverse Compton emission, with a total 2-10 keV luminosity of ∼8.0 × 1042 erg s-1. We compare 3C 220.1 with other cluster BCGs, including Cygnus A, as there are few BCGs in rich clusters hosting an FR-II galaxy.We also summarize the jet power of FR-II galaxies from different methods. The comparison suggests that the cavity power of FR-II galaxies likely underestimates the jet power. The properties of 3C 220.1 suggest that it is at the transition stage from quasar-mode feedback to radio-mode feedback.