The functional magnetic resonance imaging records signals coming from the different areas in human brains, which show activities and states of brains. These measurements result in high-dimensional time series, and each dimension represents a region in brains. In this poster, we newly propose a functional Gaussian graphical model to describe the distribution and the correlation structure of this kind of high-dimensional time series data, and we established a quadratic discriminant analysis to this functional graphical model. There are two kernel estimators introduced in our method to estimate the vertex set and the edge set of the functional graphical model, and they are used in our discriminant functions. We present a simulation study as well as two real data applications to demonstrate the performance of our method. One is an alcoholic condition detection with Electroencephalography data collected from electrodes placed on subject's scalps, and the other is a resting state detection using resting state fMRI data from the OpenfMRI database. In both applications, we we significantly beat other classification methods in accuracy. Choice of tuning parameters is also discussed.