We present a design optimization of a highly efficient light-trapping structure to significantly increase the efficiency of thin-film crystalline silicon solar cells. The structure consists of an antireflection (AR) coating, a silicon active layer, and a back reflector that combines a diffractive reflection grating with a distributed Bragg reflector. We have demonstrated that with careful design optimization, the presented light-trapping structure can lead to a remarkable cell-efficiency enhancement for the cells with very thin silicon active layers (typically 2.0-10.0 mu m) due to the significantly enhanced absorption in the wavelength range of 800-1100 nm. On the other hand, less enhancement has been predicted for much thicker cells (i.e., > 100 mu m) due to the limited absorption increase in this wavelength range. According to our simulation, the overall cell efficiency can be doubled for a 2.0-mu m-thick cell with light-trapping structure. It is found that the improvement is mainly contributed by the optimized AR coating and diffraction grating with the corresponding relative improvements of 36% and 54%, respectively. The simulation results show that the absolute cell efficiency of a 2.0-mu m-thick cell with the optimal light-trapping structure can be as large as 12%.