We design a novel light-trapping structure that can be applied to building-integrated photovoltaic systems, which inherently receive incident light asymmetrically during the whole year. The structure is optimized with respect to the asymmetric angular range of the incident light by breaking the structural symmetry. We demonstrate the effectiveness of the designed light-trapping structure for various incident-angle ranges via thorough simulation studies and experimental results using organic photovoltaic (OPV) devices. As a result, we achieved an annual energy-production enhancement of 15% in case of OPVs installed on the vertical facade of a building in Daejeon, Korea (latitude = 36.5 degrees).