In the current development of social networks, technological advancements have provided users various platforms for acquiring and disseminating information. During the process of information propagation in social networks, users can participate in multiple social networks simultaneously. Existing rumor control methods typically consider scenarios where the rumors are already known, and releasing official refutation information results in a spread of competitive information. Addressing these phenomena, we first define an Unknown Rumor Competitive Influence Minimization (UR-CIM) problem, which aims to minimize the influence of rumor propagation in a multi-layer social network environment. Subsequently, we propose an Unknown Rumor Competitive Propagation Model (URCPM), which incorporates evolutionary game theory into the linear threshold model and designs a payoff matrix to calculate the user’s benefits. Furthermore, to solve the UR-CIM problem, we design a Graph Convolutional Network method based on a Multi-layer network and Multi-Information fusion (denoted as MMI-GCN) to select protective nodes, thereby achieving rumor control effectively. Finally, we conduct experiments on three real datasets, and the results demonstrate that MMI-GCN outperforms baseline algorithms in terms of minimizing the final number of individuals influenced by rumors.