We used the lattice Boltzmann method to investigate how the hierarchical structure of a rough solid surface, which in this work is modeled as the microstructure (micropillars) covered with nanostructures (nanopillars), affects the contact angle of microdroplets atop of the solid surface and the wetting transition between the Wenzel and Cassie states. Our simulation results show that the Wenzel-to-Cassie state transition can be achieved by decreasing the fluid-solid attraction, increasing the micropillar spacing, or coating the microstructures with nanostructures. For the effect of the hierarchical structure on the contact angle, we find that the micropillars show a negligible effect on the contact angle, but they may affect the sliding angle. In contrast, it is the nanostructure that determines the contact angle. The contact angle increases with the nanopillar length until reaching a maximal value, but its dependence on the nanopillar spacing becomes more complicated. The contact angle may first increase with the nanopillar spacing and then decreases, or decreases monotonously, depending on whether the liquid enters the nanostructure or not. In this work, we also demonstrate in the presence of contact line pinning, that the pinning effect affects the apparent contact angle.