Airborne polarimetric conformal array radar has gained increased attention recently. However, the conformal array configuration and polarization factors may lead to non-stationary clutter, which significantly degrades the performance of space–time adaptive processing (STAP), particularly in short-range clutter environments. In this paper, we introduce a knowledge-aided multi-dictionary block sparse Bayesian learning (KA-MDBSBL) algorithm to improve the clutter suppression performance. Using prior knowledge, the proposed algorithm designs multi-dictionary matrices for each training sample, rather than a single dictionary matrix for the cell under test (CUT). We take advantage of the identical clutter profile under each dictionary matrix. In the multi-dictionary case, we enforce shared sparsity in the clutter profiles. Additionally, we utilize the inherent block structure of the dictionary matrix to jointly recover clutter and noise power through a fast convergence learning framework. Subsequently, the clutter plus noise covariance matrix is reconstructed using precisely estimated clutter and noise power, along with the dictionary matrix corresponding to the CUT. Numerical simulations are included to demonstrate the effectiveness and superiority of the proposed algorithm.