A new constitutive model is proposed based on the generalized three-dimensional (3D) Hoek-Brown strength criterion, which was proposed by Zhang and Zhu [1, 2]. The constitutive model involves a 3D multi-segment plasticity flow rule that can not only consider the effect of the different confining stresses on the plasticity flow rule and volumetric deformation but also need no addition uncertain parameter such as dilatancy angle. The constant volume flow rule is applied at the high confining stress condition. With the specific mathematical treatment and derivation, a new interpolation and radial flow rule is prescribed at the low confining stress and the tension condition respectively, and the continuity of plastic potential function at the principal stress space is ensured. Then the new constitutive model is implemented in the three-dimensional finite element software (GeoFBA3D). A set of numerical true triaxial compressive tests are carried out and compared with analytical solutions. Finally, a real engineering example of a highway tunnel excavated in rock masses is given for validation and application.