In passive sensing, it is crucial to develop direction-of-arrival (DOA) estimation approaches that do not depend on knowing the number of sources in advance. Wireless signals are often disrupted by impulsive noise during propagation, which undermines the performance of traditional DOA estimation approaches that assume stationary Gaussian noise. To address these challenges, we propose a robust sparse DOA estimation algorithm based on gridless variational Bayesian theory. This approach models noise as a mixture of Gaussian and generalized t distributions within a hierarchical Bayesian framework. It incorporates a noise weight factor to adapt to various noise environments. The method updates the posterior probabilities of hidden variables and model parameters using variational Bayesian inference, providing an uncertainty measure for DOAs. Experimental results show robust performance and high accuracy under low signal-to-noise ratio (SNR) conditions and limited samples.