Single-wall carbon nanotube (SWCNT) reinforced copper (Cu) matrix composites were fabricated by a simple procedure of rotating mixing and then spark plasma sintering (SPS). It was found that addition of SWCNTs as low as 0.05 wt% can increase the ultimate tensile strength (223.5 MPa) and elongation rate (48.0%) of composites by 20.8% and 57.9%, respectively, relative to those (185 MPa and 30.4%) of pure Cu material, while the composite electrical conductivity retained a high value of 94.3% International Annealed Copper Standard (IACS). Mechanism analyses revealed that there are nanometer Ni particles tightly attached to SWCNTs, which were formed in situ during SWCNT growth by arc discharge method. These nanometer Ni particles promoted the bonding between SWCNTs and Cu matrix, leading to a fracture-mode change from intergranular in pure Cu material to ductile in the composites. The related factors to influence the microstructure of composites were discussed as well.