Studies of time-varying or dynamic brain connectivity (BC) using functional magnetic resonance imaging (fMRI) are crucial to understand the relationship between different brain regions. This paper presents a novel method for estimating dynamic BC using a time-varying multivariate autoregressive (AR) model with spatial sparsity and temporal continuity constraints. The problem is formulated as a maximum a posterior probability (MAP) estimation problem and solved as a least square problem with Li-regularization for imposing the constraints. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method is employed to estimate the model parameters for making inference of dynamic BC. The proposed method was evaluated using synthetic data and visual checkerboard task experiment fMRI data. The results show that the method can effectively capture transient information transfer among visual-related brain regions whereas controlled areas not related to the process remain inactive. These verify the effectiveness and reduced variance of the proposed method for investigating dynamic task-related BC from fMRI data.