Wideband direction-of-arrival (DOA) estimation is an important task for passive sonar signal processing. Nowadays, sparse Bayesian learning (SBL) attracts much attention due to its good performance. However, performance degrades in the existence of strong interference. This problem can be solved by combining the beamformer and the SBL. The beamformer is a useful tool to suppress interference. Then, the SBL can easily estimate the DOA of the targets from the beamformer power outputs (BPO). Unfortunately, the latter step needs to compute the matrix inversion frequently, which brings some computational burden to the sonar system. In this paper, the BPO-based SBL is modified. A sequential solution is provided for the parameters in the BPO probabilistic model. In this manner, only one signal precision parameter involved in the probabilistic model is updated in each iteration and the matrix inversion is avoided during the iteration, thus reducing the computational burden. Simulation and experimental results show that the proposed method maintains high estimation precision in the interference environment. At the same time, its computational efficiency is almost three times higher in comparison with state-of-the-art methods.