In this article, we address the issues of stability and data-efficiency in reinforcement learning (RL). A novel RL approach, Kullback–Leibler divergence-regularized distributional RL (KLC51) is proposed to integrate the advantages of both stability in the distributional RL and data-efficiency in the Kullback-Leibler (KL) divergence-regularized RL in one framework. KLC51 derived the Bellman equation and the TD errors regularized by KL divergence in a distributional perspective and explored the approximated strategies of properly mapping the corresponding Boltzmann softmax term into distributions. Evaluated by several benchmark tasks with different complexity, the proposed method clearly illustrates the positive effect of the KL divergence regularization to the distributional RL including exclusive exploration behaviors and smooth value function update, and successfully demonstrates its significant superiority in both learning stability and data-efficiency compared with the related baseline approaches.