Low-temperature polycrystalline-silicon thin-film transistor (LTPS TFT) has emerged as one of the promising candidates for low-power low-cost applications on flexible substrates. In this paper, we propose a statistical simulation methodology to estimate parametric variations in scaled LTPS TFT due to the inherent properties [such as the number, location, and orientation of grain boundaries (GBs)] of the polycrystalline material. Our simulation technique employs the response surface method (RSM) to consider multiple process parameters which affect the performance distribution of LTPS TFT devices/circuits. Simulation results show that inherent GB variations result in multimodal delay distributions in basic logic building blocks (inv, nand, and nor) in scaled LTPS TFT technology, contrary to unimodal distributions in conventional bulk CMOS technology. We also observed that with increasing logic depth, the multimodal distribution converges to a unimodal distribution. Hence, to ensure robust and stable functionality of TFT technology under inherent process variations, we propose a multifinger (MF) design technique to improve the reliability of TFT circuits and to reduce the impact of GB-induced variations on TFT performance. Simulation results obtained from a 20-stage inverter chain show that by applying the proposed MF-based design, one can achieve 28% and 61% reductions in delay variations using two- and four-finger structures, respectively.