Functional alterations in the relevant neural circuits occur from drug addiction over a certain period. And these significant alterations are also revealed by analyzing fMRI. However, because of fMRI's high dimensionality and poor signal-to-noise ratio, it is challenging to encode efficient and robust brain regional embeddings for both graph-level identification and region-level biomarkers detection tasks between nicotine addiction (NA) and healthy control (HC) groups. In this work, we represent the fMRI of the rat brain as a graph with biological attributes and propose a novel feature-selected graph spatial attention network(FGSAN) to extract the biomarkers of addiction and identify from these brain networks. Specially, a graph spatial attention encoder is employed to capture the features of spatiotemporal brain networks with spatial information. The method simultaneously adopts a Bayesian feature selection strategy to optimize the model and improve classification task by constraining features. Experiments on an addiction-related neural imaging dataset show that the proposed model can obtain superior performance and detect interpretable biomarkers associated with addiction-relevant neural circuits.