In this work, we investigate the influence of grain boundaries on the performance of polycrystalline silicon thin-film transistors (poly-Si TFTs) for high resolution active-matrix organic light-emitting diode (AMOLED) displays using Voronoi diagram. The novel 2-D Voronoi polycrystalline grain structure can show a more realistic electrical parameter variability when the channel dimension is scaled down for high-resolution display. Using a proposed method, the impact of polycrystalline granular structure controlled by crystallization process is identified. Further, we predict the effect of grain boundary-induced variations under different laser annealing process, such as Excimer Laser Annealing (ELA).