Commonsense knowledge has been widely considered for building intelligent open-domain dialogue agents, aiming to generate meaningful and diverse responses. Previous works in this field usually lack the ability to effectively obtain and utilize auxiliary commonsense from the external visual world. In this paper, we argue that exploiting logical information in images related to context can be effective to enrich and steer the generation process. In view of this, we propose VICTOR, a context-relevant VIsual Commonsense enhanced dialogue generaTOR for generating coherent and informative responses. To obtain the associated visual commonsense, we devise a novel approach that expands topic words on the knowledge graph and maps them into daily scenarios. During the generation, the model adopts multimodal fusion mechanism to integrate visual and textual information, and adaptively combine their decoding distributions for better response generation. The experimental results on two public datasets show that our proposed method outperforms the latest competitive methods in terms of coherence and diversity.