Solar radiation is an important factor in the design and simulation of transparent systems. The angle-dependent optical properties of transparent systems are hard to predict because it is difficult to obtain the incidence angle of diffuse irradiance. In this paper, a normal distribution model is proposed for diffuse radiation. It is assumed that diffuse irradiance follows normal distribution. The expectation of the distribution is the incidence angle of direct radiation, while the variance is expressed as the isotropy index. Through the experimental results for a transparent double-glazing (DG) system, it is found that the values of isotropy index are related to the incidence angle of direct radiation. The normal distribution model is evaluated with the diffuse irradiance map given by the researchers in SRRL. And then the indoor diffuse irradiance through the DG system is calculated by the normal distribution model and other distribution models. The calculated results are compared with the experimental results. It is assumed that the outdoor diffuse irradiance incident on a DG system follows normal distribution. The diffuse irradiance and transmittance through a DG system are predicted by the interface energy-balance method. The predicted diffuse irradiance and transmittance by the model are compared with measured values and those predicted by other distribution models. The predicted indoor irradiance or transmittance for the proposed normal distribution model has better accuracies than the Perez and isotropic model.