Influence maximization aims at the identification of a small group of individuals that may result in the most wide information transmission in social networks. Although greedy-based algorithms can yield reliable solutions, the computational cost is extreme expensive, especially in large-scale networks. Additionally, centrality-based heuristics tend to suffer from the problem of low accuracy. To solve the influence maximization problem in an efficient way, a learning-automata-driven discrete butterfly optimization algorithm (LA-DBOA) mapped into the network topology is proposed in this paper. According to the LA-DBOA framework, a novel encoding mechanism and discrete evolution rules adapted to network topology are presented. By exploiting the asymmetry of social connections, a modified learning automata is adopted to guide the butterfly population toward promising areas. Based on the topological features of the discrete networks, a new local search strategy is conceived to enhance the search performance of the butterflies. Extensive experiments are conducted on six real networks under the independent cascade model; the results demonstrate that the proposed algorithm achieves comparable influence spread to that of CELF and outperforms other classical methods, which proves that the meta-heuristics based on swarm intelligence are effective in solving the influence maximization problem.