Tenuous subGraph finding (TGF) problem has been proposed to identify a subgraph with few social interactions and weak relationships among nodes. In particular, it aims to find a subgraph consisting of k nodes in social network G, such that the subgraph can minimize the tenuity metric. Most of the proposed techniques suffer from enormous computation due to focusing on graph-structured data. Even worse, the design of these algorithms requires manually designing suitable search strategies for specific scenarios, which is hard to be understood and implemented. To overcome these issues, this paper proposes a novel model named graph neural network with reinforcement learning for tenuous subGraph finding (R TGF), an end-to-end model combining GNN module with the reinforcement learning module, which automatically obtains the optimal solution for the tenuous subgraph. We first introduce a variant of GNN that solves the tenuity reservation problem when encoding nodes. Then we design a reward function to evaluate the node influence on subgraph tenuity. Based on this model, we can construct the solution according to the tenuity evaluations efficiently, rather than spending a high cost to compute the shortest path and enumerate all the paths between nodes. Considering the error transfer of two modules, we introduce the joint optimization strategy. Experimental results on the real-world and synthetic datasets demonstrate our proposed method R TGF outperforms existing algorithms in efficiency and solution quality.