The antireflection structure (ARS) for solar cells is categorized to mainly two different techniques, i.e., the surface texturing and the single or multi-layer antireflection interference coating. In this study, we propose a novel hybrid ARS, which integrates moth eye texturing and multi-layer coat, for application to organic photovoltaics (OPVs). Using optical simulations based on the finite-difference time-domain (FDTD) method, we conduct nearly global optimization of the geometric parameters characterizing the hybrid ARS. The proposed optimization algorithm consists of two steps: in the first step, we optimize the period and height of moth eye array, in the absence of multi-layer coating. In the second step, we optimize the whole structure of hybrid ARS by using the solution obtained by the first step as the starting search point. The methods of the simple grid search and the Hooke and Jeeves pattern search are used for global and local searches, respectively. In addition, we study the effects of deviations in the geometric parameters of hybrid ARS from their optimized values. The design concept of hybrid ARS is highly beneficial for broadband light trapping in OPVs.