In the field of underwater acoustic communication, multipath signals arrive at the receiving end with different angles and path delays, which can cause degradation in communication quality. When performing angle-delay joint estimation, sparse Bayesian learning (SBL) has many advantages over traditional methods, such as high accuracy, resolution and global minimum results, but at the cost of high computational complexity. Regarding this, in this study, we propose a low-complexity SBL based framework to jointly estimate the angle and delay of the received signal. We first propose a low-complexity approximation SBL algorithm applied to joint estimation, which can keep the super-resolution and estimation accuracy but significantly reduce the computation time. To further tackle the problem of performance degradation of the approximate algorithm in underwater low signal-to-noise ratio environments, we utilize above result as a starting point for the space-alternating generalized Expectation Maximization (SAGE) algorithm to achieve a more precise estimation. Simulation and experimental results demonstrate that the proposed algorithm has an excellent performance in various underwater multipath scenarios.