Nowadays, there is a lot of interest in assessing functional interactions between key brain regions. In this paper, Granger causality analysis (GCA) and motif structure are adopted to study directed connectivity of brain default mode networks (DMNs) in resting state. Firstly, the time series of functional magnetic resonance imaging (fMRI) data in resting state were extracted, and the causal relationship values of the nodes representing related brain regions are analyzed in time domain to construct a default network. Then, the network structures were searched from the default networks of controls and patients to determine the fixed connection mode in the networks. The important degree of motif structures in directed connectivity of default networks was judged according to p-value and Z-score. Both node degree and average distance were used to analyze the effect degree an information transfer rate of brain regions in motifs and default networks, and efficiency of the network. Finally, activity and functional connectivity strength of the default brain regions are researched according to the change of energy distributions between the normals and the patients’ brain regions. Experimental results demonstrate that, both normal subjects and stroke patients have some corresponding fixed connection mode of three nodes, and the efficiency and power spectrum of the patient's default network is somewhat lower than that of the normal person. In particular, the Right Posterior Cingulate Gyrus (PCG.R) has a larger change in functional connectivity and its activity. The research results verify the feasibility of the application of GCA and motif structure to study the functional connectivity of default networks in resting state.