With the rapid development of mobile Internet and cloud computing technology, large-scale multimedia data, e.g., texts, images, audio and videos have been generated, collected, stored and shared. In this paper, we propose a novel query problem named continuous top-$k$ geo-image query on road network which aims to search out a set of geo-visual objects based on road network distance proximity and visual content similarity. Existing approaches for spatial textual query and geo-image query cannot address this problem effectively because they do not consider both of visual content similarity and road network distance proximity on road network. In order to address this challenge effectively and efficiently, firstly we propose the definition of geo-visual objects and continuous top-$k$ geo-visual objects query on road network, then develop a score function for search. To improve the query efficiency in a large-scale road network, we propose the search algorithm named geo-visual search on road network based on a novel hybrid indexing framework called VIG-Tree, which combines G-Tree and visual inverted index technique. In addition, an important notion named safe interval and results updating rule are proposed, and based on them we develop an efficient algorithm named moving monitor algorithm to solve continuous query. Experimental evaluation on real multimedia dataset and road network dataset illustrates that our solution outperforms state-of-the-art method.