To relieve the ill-posedness of single-view x-ray luminescence computed tomography (XLCT), a fast Bayesian matching pursuit (FBMP) method combined with iterative-shrinking permissible region (ISPR) strategy was put forward.In this method, Bayesian model was combined with the greedy algorithm to quickly and efficiently restore sparse signal from few observed values. To further improve the reconstruction accuracy, FBMP was combined with ISPR strategy to simplify the mesh generation and system matrix construction by self-adaptive finite element, downsizing the factor iterative-shrinking permissible region, meanwhile relieving the ill-posedness of XLCT in reverse solution. In order to verify the effectiveness of the method, a simulation and a real physical phantom experiment were performed. The simulation results show that the proposed method, while speeding up the reconstruction process, significantly improve the localization accuracy of nano luminescent target and quantitative result of luminescence yield, which are 0.73 mm and 0.79 μg respectively. The physical phantom experiment further verifies the feasibility of this method in actual XLCT.