Copper-based Cu–1Cr-0.2Zr alloys reinforced with graphene nanosheets were fabricated via the powder metallurgy route. The alloy powders were first mechanically alloyed in a high-energy planetary ball mill up to 96 h in an argon atmosphere. Then graphene nanosheets were added (between 0 and 1 wt%) to the alloyed powder and mixed for 6 h in the milling machine. The composite powders were then consolidated in a graphite die using the spark plasma sintering (SPS) at temperatures of 650–850 °C under a vacuum atmosphere. Results showed that relative densities decreased with increasing graphene content but increased with the rising sintering temperature. The compressive yield stress of the composites increased with increasing the graphene content. The maximum yield stress was obtained with 1 wt% graphene, more than two-times increase compared with the parent alloy with no graphene addition. The contribution of the various strengthening mechanisms for the graphene-reinforced composites was calculated using a combined microstructure strengthening model based on the modified shear lag theory. The electrical conductivity enhanced as the sintering temperature was increased while it diminished with graphene addition. According to the results, the sintering temperature of 750 °C and 0.1 wt% graphene addition resulted in optimal electrical and mechanical properties.