Hoek–Brown (HB) strength criterion can reflect rock’s inherent failure nature, so it is more suitable for analyzing the stability of rock slopes. However, the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb (EMC) strength parameters instead of the nonlinear HB strength criterion. Therefore, a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework. The current method was established based on certain assumptions concing the stresses on the slip surface through amending the initial normal stress σ0 obtained without considering the effect of inter-slice forces, and it can satisfy all static equilibrium conditions of the sliding body, so the current method can obtain the reasonable and strict factor of safety (FOS) solutions. Compared with the results of other methods in some examples, the feasibility of the current method was verified. Meanwhile, the parametric analysis shows that the slope angle β has an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters. For β≤45°, both of the results are similar, showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability, but for β>60°, the differences of both the results are obvious, showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods, and then the current method should be used.