A numerical procedure to determine the equivalent hydrodynamic dispersion coefficients and Péclet number (Pe) of a fractured rock is presented using random walk particle tracking method. The geometrical effects of fracture system on hydrodynamic dispersion are studied. The results obtained from the proposed method agree well with those of empirical models, which are the scale-dependent hydrodynamic dispersion coefficients in an asymptotic or exponential form. A variance case is added to investigate the influence of longitudinal hydrodynamic dispersion in individual fractures on the macro-hydrodynamic dispersion at the fracture network scale, and its influence is demonstrated with a verification example. In addition, we investigate the influences of directional flow and stress conditions on the behavior of hydrodynamic dispersion in fracture networks. The results show that the magnitudes of the hydrodynamic dispersion coefficients are relatively smaller when the flow direction is parallel to the dip directions of fracture sets. Compressive stresses significantly reduce hydrodynamic dispersion. However, the remaining questions are: (1) whether the deformed fracture network under high stress conditions may make the scale-dependent hydrodynamic dispersion coefficients have asymptotic or exponential forms, and (2) what the conditions for existence of a well-defined equivalent hydrodynamic dispersion tensor are. They need to be further investigated.