In this paper, an l 1 -penalized maximum likelihood (ML) approach is developed for estimating the directions of arrival (DOAs) of source signals from the complex elliptically symmetric (CES) array outputs. This approach employs the l 1 -norm penalty to exploit the sparsity of the gridded directions, and the CES distribution setting has a merit of robustness to the uncertainty of the distribution of array output. To solve the constructed non-convex penalized ML optimization for spatially either uniform or non-uniform sensor noise, two majorization-minimization (MM) algorithms based on different majorizing functions are developed. The computational complexities of the above two algorithms are analyzed. A modified Bayesian information criterion (BIC) is provided for selecting an appropriate penalty parameter. The effectiveness and superiority of the proposed methods in producing high DOA estimation accuracy are shown in numerical experiments.