Causal discovery from observational data is a fundamental problem in science. Though the linear non-Gaussian acyclic model (LiNGAM) has shown promising results in various applications, it still faces the following challenges in the data with multiple latent confounders: 1) how to detect the latent confounders and 2) how to uncover the causal relations among observed and latent variables. To address these two challenges, we propose a hybrid causal discovery method for the LiNGAM with multiple latent confounders (MLCLiNGAM). First, we utilize the constraint-based method to learn the causal skeleton. Second, we identify the causal directions, by conducting regression and independence tests on the adjacent pairs in the causal skeleton. Third, we detect the latent confounders with the help of the maximal clique patterns raised by the latent confounders and reconstruct the causal structure with latent variables. Theoretical results show the correctness and efficiency of the algorithms. We conduct extensive experiments on synthetic and real data, which illustrates the efficiency and effectiveness of the proposed algorithms.