By the use of multi-pinhole random screens, the intensity and phase distributions of speckle fields are analyzed. It is found that the distribution of phase vortices shows local similarity and the cluster phenomena appearing in local regions. There are many independent units composed by 2, 4 and 6 positive and negative phase vortices. These new phenomena are different from those generated by a single square aperture random screen. The density of phase vortices becomes larger with the increase of the distance between pinholes and the number of pinholes.