Condensation of liquid droplets on solid surfaces happens widely in nature and industrial processes. This phase-change phenomenon has great effect on the performance of some microfluidic devices. On the basis of micro- and nanotechnology, superhydrophobic structured surfaces can be well-fabricated. In this work, the nucleating and growth of droplets on different structured surfaces are investigated numerically. The dynamic behavior of droplets during the condensation is simulated by the multiphase lattice Boltzmann method (LBM), which has the ability to incorporate the microscopic interactions, including fluid-fluid interaction and fluid-surface interaction. The results by the LBM show that, besides the chemical properties of surfaces, the topography of structures on solid surfaces influences the condensation process. For superhydrophobic surfaces, the spacing and height of microridges have significant influence on the nucleation sites. This mechanism provides an effective way for prevention of wetting on surfaces in engineering applications. Moreover, it suggests a way to prevent ice formation on surfaces caused by the condensation of subcooled water. For hydrophilic surfaces, however, microstructures may be submerged by the liquid films adhering to the surfaces. In this case, microstructures will fail to control the condensation process. Our research provides an optimized way for designing surfaces for condensation in engineering systems.