The generalized-stacking-fault-energy (GSFE) curve for pure Cobalt and Co-9 at.% X solid-solution alloys (X = Cr, W, Mo, Ni, Mn, Al, Fe) have been successfully calculated by rigidly shearing an fcc crystal at a (1 1 1) plane along a [1 1 −2] slip direction in two processes using first-principles density-functional-theory (DFT), provide a highly accurate modeling and a fairly good agreement with available experimental and other theoretical results in the literature. The objectives of this study are to provide a useful guideline for the Co-based alloy design with superior performances and new insight for understanding the nature of the fcc to hcp phase transformation. Evaluation of the GSFE values is based on the ratio of the stable and unstable stacking fault energy, the twinnabilities with three criterions for crack tip twinning, grain boundary twinning and inherent twinning, as well as the predicted critical twinning stress. It concludes that alloying with Cr, W and Mo atoms are expected to bring a significant increase in the tendency of the dominant deformation mechanism for the formation of partial dislocations and mechanical twinning of pure Co. The investigation regarding the electronic structure, such as interlayer distance distortion between a faulted and perfect fcc structure, atomic bonding, charge density distributions and density of states (DOS) in the present work can describe why and how alloying atoms change the GSFE values of Co-based alloys. [ABSTRACT FROM AUTHOR]