Organic solar cells are attractive for various applications with their flexibility and low-cost manufacturability. In order to increase their attractiveness in practice, it is essential to improve their energy conversion efficiency. In this work, semi-cylindrical-shell-shaped structures are proposed as one of the approaches, aiming at absorption enhancement in an organic solar cell. Poly(3-hexylthiophene-2,5-diyl) blended with indene-C60 bisadduct (P3HT:ICBA) is considered as the active layer. Light coupling to the guided modes and a geometrical advantage are attributed to this absorption enhancement. Finite-difference time-domain methods and finite element analysis are used to examine the absorption spectra for two types of devices, i.e., a debossed type and an embossed type. It is shown that absorption enhancement increases as the radius of the cylinder increases, but reaches a saturation at about 4-µm radius. The average absorption enhancement with an active layer thickness of 200 nm and radius of 4 µm, and for incidence angles between 0° and 70°, is found as 51%-52% for TE-polarized input and as 30%-33% for TM-polarized input when compared to a flat structure. Another merit of the proposed structures is that the range of incidence angles where the integrated absorption is at the level of the normal incidence is significantly broadened, reaching 70°-80°. This feature can be highly useful especially when organic solar cells are to be placed around a round object. The study results also exhibit that the proposed devices bear broadband absorption characteristics.