Refractory high entropy alloys (HEAs) have excellent thermal stability, good strength and toughness, which have great potential application as a second phase in improving microstructure and properties of metal matrix. Here, refractory HEA WTaMoNb is introduced into Cu matrix to synthesize WTaMoNb/Cu nanocomposite by two-step mechanical alloying (MA) and hot pressing sintering (HPS), which owns BCC/FCC structure. During MA, WTaMoNb is firstly prepared and then milled with Cu. Then, WTaMoNb/Cu nanocomposite is synthesised via HPS. The sintered Cu-10wt.%WTaMoNb alloy displays an excellent thermal stability, a high tensile strength of 758.3 ± 20.8 MPa, and an electrical conductivity of 42.5 ± 1.5% international annealed copper standard (IACS).