A lens-less method for generating vortex arrays with tunable parameters is proposed based on quasi-Talbot effects. By illuminating a two-dimensional periodic sinusoidal grating with a vortex beam carrying a fourth-order cross-phase, the continuous vortex array structure can be generated in the Fresnel diffraction region. Due to the shaping effect of the fourth-order cross-phase on the vortex beam, by changing the constant parameter of the fourth-order cross-phase, it is possible to shape the generation of optical vortex arrays at different positions. This will somewhat broaden the flexibility of the lens-free optical vortex array in terms of generation position. In addition, the generation of polygonal optical vortex arrays is achieved by higher-order cross-phases of different orders. This technique has potential applications in various fields such as optical tweezers, multi-particle screening, microscopic manipulation, etc.