An fMRI connectivity analysis approach combining both principal component analysis (PCA) and Granger causality method (GCM) is proposed to study directional influence between functional brain regions. Both simulated data and human fMRI data obtained during behavioral tasks were used to validate this method. If PCA is first used to reduce number of fMRI time series, then more energy and information features in the signal can be preserved than using averaged values from brain regions of interest. Subsequently, GCM can be applied to principal components extracted in order to further investigate effective connectivity. The simulation demonstrated that by using GCM with PCA, between-region causalities were better represented than using GCM with average values. Furthermore, after localizing an emotion task-induced activation in the anterior cingulate cortex, inferior frontal sulcus and amygdala, the directional influences among these brain regions were resolved using our new approach. These results indicate that using PCA may improve upon application of existing GCMs in study of human brain effective connectivity.