Flexural toppling failure is a widespread issue in anti-dip bedding rock slopes. Rock bolts are usually employed to reinforce bedding rock slopes as they are low-cost and efficient. In this technical note, a mechanical model based on limit equilibrium theory is proposed to predict the stability of anti-dip bedding rock slopes locally reinforced by rock bolts. By considering a practical case, the proposed model is subsequently verified by comparing its results with numerical results using a discrete element method. Finally, we investigate the influence the positions of rock bolts have on the reinforcement effect. The results show that, for a given bolt angle, the reinforcement effect is controlled by the positions of the rock bolts. In particular, the installation position must start from the superimposed toppling zone (the zone within which the rock layers resemble superimposed cantilever beams). On the other hand, there is no reinforcement effect if the installation position starts from the cantilevered toppling zone (the zone within which the rock layers resemble individual cantilever beams). The method proposed provides theoretical guidance for the design of the reinforcements applied to anti-dip bedding rock slopes. The results produced should also help engineers to gain a better understanding of the reinforcement mechanisms underlying the action of the rock bolts used in anti-dip bedding rock slopes. •A theoretical model reflecting the effect of local rock bolts is proposed.•Reinforcement effect of rock bolts relies on the reinforcement position.•Influence of the height of rock layer on the reinforcement effect is discussed.