The situation that a two-level atom is trapped in each cavity, the two cavities are connected via a fiber, and each atom resonantly interacts with cavity is considered. Geometrical quantum discord (GQD) is used to quantify the degree of correlation between two subsystems, and the GQDs between two atoms and between two cavities in T-shaped coupling cavity system are analyzed. The influences of the atom-cavity and fiber-cavity coupling intensities on GQD are discussed by using the numerical calculation method. The research results show that, with the increase of the atom-cavity coupling coefficient, the GQD between atoms is weakened, but the GQD between cavities is strengthened. With the increase of fiber-cavity coupling coefficient, the GQD between atoms is strengthened, but the GQD between cavities is weakened.