A new multiaxial high-cycle fatigue criterion based on the so-called critical plane approach is presented. According to such a criterion, the critical plane orientation is proposed to be correlated with the averaged principal stress directions deduced through the weight function method. Then the fatigue failure assessment is performed by considering a nonlinear combination of the maximum normal stress and the shear stress amplitude acting on the critical plane. The proposed criterion is applied to a general sinusoidal biaxial stress state, for which analytical formulae can be derived. The theoretical results calculated according to the present criterion, together with those of other common critical plane criteria, are compared with experimental data related to different brittle (hard) metals under in-phase or out-of-phase sinusoidal biaxial normal and shear stress states.