The Mohr-Coulomb (M-C) stress criterion is widely applied to describe the pressure sensitivity of bulk metallic glasses (BMGs). However, this criterion is incapable of predicting the variation in fracture angles under different loading modes. Moreover, the M-C criterion cannot describe the plastic fracture of BMGs under compressive loading because the nominal stress of most BMGs remains unchanged after the materials yield. Based on these limitations, we propose a new generalized M-C strain criterion and apply it to analyze the fracture behaviors of two typical Zr-based BMG round bar specimens under complex compressive loading. In this case, the predicted initial yielding stress is in good agreement with the experimental results. The theoretical results can also describe the critical shear strain and fracture angle of BMGs that are associated with the deformation mode.