The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase pattes produced by the two-pinhole aperture, whose phase distributions appear as striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.