Based on the four-cylindrical-lens slit spatial filter proposed by American Lawrence Livermore National Laboratory, the beam propagation characteristics in the slit spatial filter has been studied with Rayleigh-Sommerfeld diffraction integral and commercial Matlab software on image relay and spatial filtering. Unlike the conventional pinhole spatial filter, the front (back) focal plane of the slit spatial filter system is not only related with focal length, but also with the distance between the cylindrical lenses, which is beneficial for greatly decreasing the focal intensity in high-power lasers by about 3 orders of magnitudes and greatly decreasing the scale of the spatial filter. However, with the slit spatial filter, negative point is also brought about that, the image relay of slit spatial filter can be strict satisfied only in the situation of 1 time beam expansion. In the situation of 1 times beam expansion, the spatial filtering of the slit spatial filter is consistent with the conventional pinhole spatial filter.