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A four-layered W/Cu functionally graded material (FGM) (W90% + Cu10%/W80% + Cu20%/W70% + Cu30%/W60% + Cu40%, wt.% fraction) and a four-layered diamond/W–Cu FGM (W90% + Cu10%/W80% + Cu20%/W70% + Cu30%/W55% + Cu40% + diamond5%, wt.% fraction) were fabricated by microwave sintering. The thermal conductivity and thermal shock resistance of diamond/W–Cu FGM and W–Cu FGM were investigated. The morphologies of the diamond particles and different FGMs were analyzed using AFM, SEM, EDS, and TEM. The results show that a 200 nm rough tungsten coating was formed on the surface of the diamond. The density of the tungsten-coated diamond/W–Cu FGM, obtained by microwave sintering at 1200 °C for 30 min, was 94.66%. The thermal conductivity of the four-layered diamond/W–Cu FGM was 220 W·m-1·K-1, which is higher than that of the four-layered W/Cu FGM (209 W m−1 K−1). This indicates that adding an appropriate amount of tungsten-coated diamond to the high Cu layer W/Cu FGM improves the thermal conductivity of the composite. The diamond/W–Cu FGM sintered at 1200 °C for 10 min exhibited better thermal shock resistance than diamond/W–Cu FGM sintered at 1100 °C for 10 min.