In this work, the generalized stacking fault energies (GSFEs) of {10-11}<11-23> slip system in a wide range of Mg-X (X = Ag, Al, Bi, Ca, Dy, Er, Gd, Ho, Li, Lu, Mn, Nd, Pb, Sc, Sm, Sn, Y, Yb, Zn and Zr) binary alloys has been studied. The doping concentration in the doping plane and the Mg-X system is 12.5 at.% and 1.79 at.%, respectively. Two slip modes (slip mode I and II) were considered. For pure magnesium, these two slip modes are equivalent to each other. However, substituting a solute atom into the magnesium matrix will cause different effects on these two slip modes. Based on the calculated GSFEs, two design maps were constructed to predict solute effects on the behavior of the {10-11}<11-23> dislocations. The design maps suggest that the addition of Ag, Al, Ca, Dy, Er, Gd, Ho, Lu, Nd, Sm, Y, Yb and Zn could facilitate the {10-11}<11-23> dislocations.