The Hoek-Brown(HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass,while evolving ever since.However,negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version.At the same time,several three-dimensional(3D) HB strength,which can takes into account the influence of the intermediate principal stress,have already been proposed,among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one.However,the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface.In this paper,a new 3D HB strength criterion is presented based on a generalized form of the HB criterion,which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion.In addition,this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion.Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion.The results show that this new criterion may over-predict or underpredict the polyaxial strength of rocks but the errors are relatively small,and similar results are also found for the Zhang 3D HB criterion,which one is better depends on the type of the rock under estimation. The Hoek-Brown (HB) strength criterion has been a widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. Despite, negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version. At the same time, several three-dimensional (3D) HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one .However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. addition, this new criterion can remedy to some ext ent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and leads it with the Zhang 3D HB criterion. results show that this new criterion may over-predict or underpredict the polyaxial strength of rocks but the errors are relatively small, and similar results are also found for the Zhang 3D HB criterion, which one is better than on the type of the rock under estimation.