As a typical type of three-dimensional compound parabolic concentrator (CPC), dielectric crossed compound parabolic concentrator (dCCPC) has drawn a significant research attention in these years to explore its angular characteristics in solar collection for concentrating photovoltaics and daylighting control in buildings. Optical efficiency and transmittance are the main performance indicators to evaluate a dCCPC which may be base coated as a receiver or non-coated for daylighting. The most common way to accurately determine the performance of a dCCPC is through ray-tracing simulation which requires advanced optical analysis software and lots of time. To facilitate the annual performance evaluation of dCCPC, this study puts forward several mathematical models for multiple nonlinear regression based on a mass of simulation results. The models can predict the transmittance of non-coated dCCPC and the both of transmittance and optical efficiency of base-coated dCCPC from several sky parameters, respectively. The agreement between predicted and simulated values is generally satisfactory. The coefficient of determination (R-2) for each model is higher than 0.94 and the mean square error (MSE) is less than 0.002. Six specific time among the whole year are selected to verify the reliability of the prediction models in practice. The limitation and significance of these models are discussed as well. The regression models provide a convenient and accurate approach to predict the optical performance of dCCPC.