Underdetermined direction-of-arrival (DOA) estimation for wideband signals by sparse arrays is discussed in the framework of sparse Bayesian learning (SBL). The problem is transformed to recovering multiple nonnegative sparse vectors, which share the same sparse support but correspond to distinct overcomplete basis matrices, from their noise contaminated linear combination vectors. A two-layer Bayesian model is established, and a hyperparameter vector, which reveals the true DOAs, is set to control this common sparsity in the model. The expectation-maximization algorithm is employed to realize this joint nonnegative SBL procedure, which can give the DOA estimation in a few iterations. The proposed method manifests mild computational complexity, and numerical simulation results show that compared with the existing underdetermined DOA estimation methods, it yields superior estimation accuracy, without the prior knowledge of number of sources.