Studying causality relationships between different brain regions using the fMRI method has attracted great attention. To investigate causality relationships between different brain regions, we need to identify both the brain network structure and the influence magnitude. Most current methods concentrate on magnitude estimation, but not on identifying the connection or structure of the network. To address this problem, we proposed a nonlinear system identification method, in which a polynomial kernel was adopted to approximate the relation between the system inputs and outputs. However, this method has an overfitting problem for modelling the input-output relation if we apply the method to model the brain network directly. To overcome this limitation, this study applied the least absolute shrinkage and selection operator (LASSO) model selection method to identify both brain region networks and the connection strength (system coefficients). From these coefficients, the causality influence is derived from the identified structure. The method was verified based on the human visual cortex with phase-encoded designs. The functional data were pre-processed with motion correction. The visual cortex brain regions were defined based on a retinotopic mapping method. An eight-connection visual system network was adopted to validate the method. The proposed method was able to identify both the connected visual networks and associated coefficients from the LASSO model selection. The result showed that this method can be applied to identify both network structures and associated causalities between different brain regions. System identification with LASSO model selection algorithm is a powerful approach for fMRI effective connectivity study.