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Both electronic and ionic conductivities are of high importance to the performance of anode materials for Li-ion batteries. Many large capacity anode materials (such as Ge) do not have sufficiently high electronic and ionic conductivities required for high-rate cycling. Here, we report a novel ternary compound, copper germanium phosphide (CuGe2P3), as a high-rate anode. Being synthesized via a facile and scalable mechanochemistry method, CuGe2P3 has a cation-disordered sphalerite structure and offers higher ionic and electronic conductivities and better tolerance to volume change during cycling than Ge, as confirmed by first principles calculations and experimental characterization, including high-resolution synchrotron X-ray diffraction, HRTEM, SAED, XPS and Raman spectroscopy. Furthermore, the results suggest that CuGe2P3 has a reversible Li-storage mechanism of conversion reaction. When composited with graphite by virtue of a two-stage ball-milling process, the yolk–shell structure of the amorphous carbon-coated CuGe2P3 nanocomposite (CuGe2P3/C@Graphene) delivers a high initial coulombic efficiency (91%), a superior cycling stability (1312 mA h g−1 capacity after 600 cycles at 0.2 A g−1 and 876 mA h g−1 capacity after 1600 cycles at 2 A g−1), and an excellent rate capability (386 mA h g−1 capacity at 30 A g−1), surpassing most Ge-based anodes reported to date. Moreover, a series of cation-disordered new phases in the Cu(Zn)–Ge–P family with various cation ratios offer similar Li-storage properties, achieving high reversible capacities with high initial coulombic efficiencies and desirable redox chemistry with improved safety.