Neural generation models have shown great potential in conversation generation recently. However, these methods tend to generate uninformative or irrelevant responses. In this paper, we present a novel topic-enhanced controllable CVAE (TEC-CVAE) model to address this issue. On the one hand, the model learns the context-interactive topic knowledge through a novel multi-hop hybrid attention in the encoder. On the other hand, we design a topic-aware controllable decoder to constrain the expression of the stochastic latent variable in the CVAE to reduce irrelevant responses. Experimental results on two public datasets show that the two mechanisms synchronize to improve both relevance and diversity, and the proposed model outperforms other competitive methods.