Speckle patterns can be very promising for some applications due to their unique properties. This paper presents the possibility of numerically and experimentally formation of speckle patterns using broadband THz radiation. Strong dependence of the statistical parameters of speckles, such as size and sharpness on the parameters of the diffuser are demonstrated: the correlation length and the mean square deviation of the phase surface inhomogeneity. As the surface correlation length increasing, the speckle size increases and its sharpness decreases. Alternatively, increasing of the surface height standard deviation leads to a speckle size decreasing and sharpness increasing. The dimensions of the individual experimentally formed speckles correspond to obtained results of numerical simulation. The possibility of the formed speckle patterns application for the implementation of the ghost imaging technique has been demonstrated by methods of numerical modeling.