Many important application scenarios in the future fifth generation (5G) systems, such as indoor navigation and autonomous driving, rely on accurate localization of users. In this paper, we propose a sparse-Bayesian-inference (SBI) based direct location algorithm for massive MIMO systems, which can exploit the sparse and high-resolution nature of angle of arrival (AoA) and any available statistical location information (SLI), to significantly improve the user localization accuracy. The existing common methods in SBI, such as approximate message passing (AMP) an variational Bayesian inference (VBI), may not work well for the massive MIMO localization problem due to their respective drawbacks. To overcome these drawbacks, we first propose a novel three-layer hierarchical structured (3LHS) sparse prior model to incorporate both the structured sparsity of the massive MIMO channel and the SLI into the SBI-based localization formulation. Then we propose a structured VBI algorithm called 3LHS-VBI to solve the resulting SBI-based localization problem. Finally, simulations verify the superior performance of the proposed location algorithm.