Although tailoring stacking fault energy (SFE) through the addition of suitable alloying element can improve mechanical properties, the effect of strain must also be included to account for the Co-based alloy design. Using first-principles density-functional-theory calculations, we revealed that there is a strong effect of the strain (volumetric strain, simple strain, and volume conserving) and external pressure on the intrinsic SFE of face-centered cubic (fcc) cobalt. This result indicated a new insight into the Co-based alloys design, especially for application at high pressure and severe plastic deformation. The intrinsic SFE decreased by increasing tensile strain or decreasing pressure, thus the tendency of forming stacking faults increases which improves the mechanical properties. Effect of volumetric (hydrostatic) strain is the strongest indicated that the volume is the dominant factor in determining the SFE and the strain-induced fcc-hcp phase transformation. Different strain methods give different charge transfer between adjacent atoms and then contribute to the variation of the atomic bonding at the specific direction and SFE behavior. Application of external pressure from 0 to 15 GPa increased the elastic constants and elastic modulus of fcc Co and then improved the ductility.