Accurate and efficient approaches to predict the optical properties of organic semiconducting compounds could accelerate the search for efficient organic photovoltaic materials. Nevertheless, predicting the optical properties of organic semiconductors has been plagued by the inaccuracy or computational cost of conventional first-principles calculations. In this work, we demonstrate that orbital-dependent density-functional theory based upon Koopmans' condition [Phys. Rev. B, 2010, 82, 115121] is apt for describing donor and acceptor levels for a wide variety of organic molecules, clusters, and oligomers within a few tenths of an electron-volt relative to experiment, which is comparable to the predictive performance of many-body perturbation theory methods at a fraction of the computational cost.