Direction of arrival (DOA) estimation, as the main technology of passive radio monitoring and positioning, has been deeply investigated. However, the DOA for distributed sources is challenging to estimate in environments with impulsive noise. Although many methods have been proposed for DOA estimation, most of them assume that array output signals contain Gaussian noise. Therefore, the performance of these methods is often poor for alpha-stable distributed impulsive noise. Furthermore, subspace-based DOA estimation methods for distributed sources require a two-dimensional (2D) peak search, which increases the consumption of system computing resources. In this paper, a Q-function-based kernel function is proposed, and its properties are derived. On this basis, a novel DOA estimation method is proposed for coherently distributed (CD) sources in impulsive noise. To reduce computational complexity, a Lagrangian quadratic optimization function is derived by approximating the generalized array manifold of the CD source. By solving this optimization function, a 2D peak search can be reduced to several one-dimensional (1D) peak searches. The simulation results illustrate that the accuracy and robustness of the proposed method outperform those of existing methods.