Direct normal irradiance (DNI) is vital for concentrated solar thermal plants, and its value under clear sky condition is usually used as an important input of some forecasting models for solar irradiance. First of all, a semi-empirical model is developed for calculating the clear-sky DNI, and it is used to transform DNI into clear-sky index to remove the impact of the sun's position on DNI. Then, a wavelet forecasting model, using the clear-sky index as input, is proposed for estimating the inter-hour DNI under any sky conditions. The non-stationary series of the clear-sky index is decomposed by wavelet technology to obtain four sub-series with different frequencies, and forecasting sub-models are constructed according to the features of corresponding sub-series, respectively. Finally, model validation is conducted with data from the open database of the National Renewable Energy Laboratory. The result shows that the performance of the clear-sky model is satisfactory comparing with some other published clear-sky models, and that the wavelet forecasting model achieves great performance with nMAE = 0.84-7.66% and nRMSE = 1.89-10.99% for four different stations and also outperforms other published forecasting models. (C) 2016 Elsevier Ltd. All rights reserved.