Gaussian beam resonance system (GBRS) opens a very important window for detection of relic stochastic high frequency gravitational waves (HFGWs) of early universe. The results of calculation show that the first-order perturbation photon flux produced by this system has no observable effect when the GWs frequency is different from that of Gaussian beam. The first-order perturbation photon flux produced by GBRS will be reduced by several orders of magnitude when the propagation direction of GWs is different from that the positive direction of the symmetrical axis of Gaussian beam, i. e., GBRS only responds to relic HFGWs that propagate along a specific direction. Therefore, GBRS have a useful selective effect with respect to the frequency and propagation direction of relic HFGWs.