The behavior of wave front of acoustic wave, propagating in a model of fractured media, is studied. The locations and orientations of fractures are randomly distributed. By numerical simulation of acoustic wave propagation in fractured media, the effects of geometrical properties of the medium, i.e., fractures number density and fractures width, on dynamical properties as wave front (WF) roughness, correlation function, and correlation length, are studied. The WF exhibits self-affine properties, with given roughness exponent evolving during the time. The correlation length of the wave front increases with time, and its value is in same order of magnitude with length of fractures in the medium. The WF roughness shows a scaling relation with respect to the fractures number density.