We report on what is, to the best of our knowledge, the first ultra-efficient 1.5 μm Raman amplifier in a methane-filled anti-resonance hollow-core fiber. A 1.5 μm single frequency seed laser is coupled into the hollow-core fiber together with a 1064 nm pulsed pump laser using a shortpass dichromic mirror, and then amplified by stimulated Raman scattering of methane. A maximum optical-to-optical conversion efficiency of 66.4% has been obtained, resulting in a record near quantum-limit efficiency of 96.3% in a 2 m long hollow-core fiber filled with only 2 bar methane gas. This kind of gas filled hollow-core Raman amplifier provides a potential method to obtain high efficiency mid-infrared laser sources with low threshold and narrow linewidth in various applications.