The evolution of microstructure and crystallographic texture in Cu–1Cr-0.061Zr alloy strips during multi-pass cold rolling deformation was studied. The results showed that the tensile strength of Cu–1Cr-0.061Zr alloy increased from 507 MPa to 683 MPa with increasing rolling strain, while the conductivity decreased from 84.1 to 68.1 of the International Annealed Copper Standard. When the strain is 1.86–3.85, the elongation is effectively stable at 7.5%–8.5%. The local strain and grain dislocation angle inside the alloy gradually increase with the increase in strain, and the grain orientation distribution becomes more uniform and stronger. The dislocation slip generated during the rolling process leads to the concentration of grain orientation toward the <11−1> direction, causing the Goss texture ({110}<001>) to gradually transform into a Copper texture ({112}<11−1>) with relatively stable grain orientation, which significantly improves the mechanical properties at the macro level. In addition, the heat generated during the cold rolling process causes the cancellation of heterologous dislocations on a certain slip surface, resulting in a decreased dislocation density and a slight growth of nanoprecipitates. Nanoprecipitation strengthening and grain boundary strengthening are the main strengthening mechanisms in the Cu–1Cr-0.061Zr alloy, while the strength contribution of banded Cr phase dispersion is relatively small.