This article addresses the problem of estimating brain effective connectivity from electroencephalogram (EEG) signals using a Granger causality (GC) characterized on state-space models, extended from the conventional vector autoregressive (VAR) process. The scheme involves two main steps: model estimation and model inference to estimate brain connectivity. The model estimation performs a subspace identification and active source selection based on group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a Riccati equation for the covariance of estimation error. We verify the performance on simulated datasets that represent realistic human brain activities under several conditions, including percentages and location of active sources, and the number of EEG electrodes. Our model's accuracy in estimating connectivity is compared with a two-stage approach using source reconstructions and a VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. When the method was applied to a real EEG SSVEP dataset, the temporal lobe was found to be a mediating connection between the temporal and occipital areas, which agreed with findings in previous studies.