Abstract: The Hoek-Brown strength criterion is widely used in the field of rock engineering, but its application in the brittle-to-ductile transition of deep rock is relatively limited. A study on the improvement of the Hoek-Brown strength criterion considering the critical state for rock brittle-to-ductile transition is conducted to further investigate the application of this criterion in deep rock engineering and provide a suitable criterion for judging the critical state of brittle-to-ductile transition for deep rock. Based on the characteristics of the critical state for rock brittle-to-ductile transition, and in response to the current situation where the critical confining pressure σ_3cr for rock brittle-to-ductile transition is overly simplified by using only the multiple relationship of the uniaxial compressive strength σ_c, a multi-parameter critical confining pressure σ_3cr-M included the fracture tip stress, uniaxial tensile strength, similar internal cohesion, and fracture angle is proposed in combination with the Mohr-Wedge criterion. The rationality of the rock critical state confining pressures is preliminarily discussed in the Mohr-Wedge criterion by utilizing the twelve sets of rock conventional triaxial compression test data. The results indicate that the multi-parameter σ_3cr-M is more reasonable than the parameter σ_3cr that only considers the uniaxial compressive strength. The suitable critical confining pressure for the critical state of rock brittle-to-ductile transition should make the rock strength criterion meet two conditions: the mean absolute error of rock strength fitting is less than 5%; the criterion function is continuously derivable at the critical point of rock brittle-to-ductile transition. Subsequently, considering the strength curve is easy to appear the corner points at the critical point of rock brittle-to-ductile transition, an improved Hoek-Brown criterion including the critical confining pressure of rock brittle-to-ductile transition is proposed. Then, the applicability of the improved Hoek-Brown criterion is demonstrated in detail through the characteristics of the strength curve and the fitting error analysis. The results show that the strength curves of the improved Hoek-Brown criterion corresponding to the different critical confining pressures are continuously derivable at the critical point of rock brittle-to-ductile transition. The improved Hoek-Brown criterion based on the multi-parameter σ_3cr-M has the smallest mean absolute error (1.683 0%) of fitting and better conforms to the trend of rock brittle-to-ductile transition, which is significant superiority in predicting the rock brittle-to-ductile transition compared to the Hoek-Brown criterion for intact rocks. The research findings provide a valuable reference for the application of the Hoek-Brown criterion in the brittle-to-ductile transition of deep rock.