Using a fast hot press sintering technique, Cu/graphite composites doped with MoAlB ceramic particles were synthesized. The impact of varying sintering temperatures on the composites' mechanical, tribological, and microstructure characteristics were studied. The Al element diffused from the MoAlB particles into the copper matrix and produced the MoB phase when the sintering temperature rose over 850 °C. The formation of MoB phase, which was well bound to the matrix, and the formation of Cu(Al) solid solution could improve the plastic deformation resistance of the composites. This, along with the lubrication supplied by graphite, synergistically improved the mechanical and frictional properties of Cu/graphite composites. The composites exhibited remarkable wear resistance (the wear rate was reduced to 3.36 × 10−5 mm3·N−1·m−1) and high compressive strength (266.25 MPa) when the sintering temperature was set to 900 °C. In order to create high-performance copper-based self-lubricating composites, this effort may offer a new research direction.