Designed microtextured surfaces have shown promising applications in tuning the wettability of a liquid droplet on the surfaces and attracted great attention over the past decade; unfortunately, the effect of surface geometry on wetting properties is still poorly understood. In this work, two- and multi-stage pillar microtextures are designed to construct gradient surfaces by altering pillar width and spacing. Then, the multi-phase lattice-Boltzmann method (LBM) is used to investigate the wetting dynamics of a liquid droplet on the gradient surface. Results show that for the two-stage gradient surface with variable pillar spacing, the contact angle hysteresis is found to be proportional to the roughness gradient when droplet/surface system is in the Cassie-Baxter state. However, this proportional relation is no longer correct when the system is in the transition state between the Wenzel and Cassie-Baxter states. For the two-stage gradient surface with variable pillar spacing, the contact angle hysteresis always increases linearly with increasing roughness gradient. Results also show that when a larger droplet is placed on the multi-stage gradient surface, stronger droplet motion is observed due to the smaller contact angle hysteresis. The present LBM simulations provide a guideline for the design and manufacture of the microtextured surfaces to tune the droplet wettability and motion.