The material strengths of polycrystalline metals have been widely predicted according to the grain size, where yield stress is governed by slip transfer through the grain boundary (GB). The transferability of a dislocation across a GB is enormously important in the deformation process as well as the interaction between a dislocation and GB. This paper proposes a new criterion for the transferability of dislocations through a GB that considers both the intergranular crystallographic orientation of slip systems and the applied stress condition. Atomistic simulations were carried out to investigate the slip transfer event of simple bicrystals composed of Σ3(1̄12) GB than Σ3(1̄11) GBs under uniaxial deformation and to illustrate the availability of this criterion. As a result, in contrast to the predictions of conventional criteria such as the M-value, dislocations propagated more easily across the Σ3(1̄11) and Σ3(1̄12) GB under given stress states, reflecting a larger L′-value of Σ3 bicrystal associated with higher transferability.