The structure, chemical and phase compositions, and hardness of a Cu–Ti–C–B composite prepared by self-propagating high-temperature synthesis (SHS) are studied. The composite matrix is shown to be a copper-based solid solution (γ), and the strengthening phases are TiC and TiB2, which are nonuniformly distributed over the composite volume. The microhardness of solid solution regions is 450 HV 0.05; the microhardness of (γ + TiC) regions is 760 HV 0.1, whereas the microhardness of (γ + TiB2) regions with a predominance of TB2 particles is 1042 HV 0.1. The integral hardness of the composite is 62 HRC. The nonuniform distribution of filling material particles in the composite bulk determines the nonuniformity of micromechanical properties. The (γ + TiB2) regions of the composite are the strongest structural component, which are characterized by the high modulus of elasticity, work of elastic recovery, and arbitrary wear resistance HIT/E. The abrasive wear resistance of the Cu–Ti–C–B composite is comparable with that of a Fe‒Ti–C–B composite. In this case, the surface roughness of the Cu–Ti–C–B composite after tests is minimum; this is related to the higher plasticity of the Cu-based solid solution. The wear of the composite occurs via the plastic edging mechanism.