Inferring effective connectivity between spatially segregated brain regions is important for understanding human brain dynamics in health and disease. Non-invasive neuroimaging modalities, such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), are often used to make measurements and infer connectivity. However most studies do not consider integrating the two modalities even though each is an indirect measure of the latent neural dynamics and each has its own spatial and/or temporal limitations. In this study, we develop a linear state-space model to infer the effective connectivity in a distributed brain network based on simultaneously recorded EEG and fMRI data. Our method first identifies task-dependent and subject-dependent regions of interest (ROI) based on the analysis of fMRI data. Directed influences between the latent neural states at these ROIs are then modeled as a multivariate autogressive (MVAR) process driven by various exogenous inputs. The latent neural dynamics give rise to the observed scalp EEG measurements via a biophysically informed linear EEG forward model. We use a mean-field variational Bayesian approach to infer the posterior distribution of latent states and model parameters. The performance of the model was evaluated on two sets of simulations. Our results emphasize the importance of obtaining accurate spatial localization of ROIs from fMRI. Finally, we applied the model to simultaneously recorded EEG-fMRI data from 10 subjects during a Face-Car-House visual categorization task and compared the change in connectivity induced by different stimulus categories.