Strength anisotropy in soils needs to be characterized by proper anisotropic failure criterion. This paper presents a novel yet simple methodology to generalize an isotropic failure criterion to account for strength anisotropy in soils. A salient ingredient of the method involves the introduction of the degree of cross anisotropy and an anisotropic variable, defined by the joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, into the frictional characteristic of the isotropic criterion. The well-received Lade's failure criterion is taken as an example to demonstrate the generalization. Predictions using the newly generalized Lade's criterion for a number of soils, including completely decomposed granite, glass beads (virtual sand), natural clays, sand, as well as silty sand, show good agreement with test data. The proposed approach has proved to be simple and generic, and can be effortlessly applied to many existing isotropic failure criteria to adapt them to account for strength anisotropy. The treatment also requires very few parameters, which can be conveniently calibrated from conventional laboratory tests in most cases.