To address the serious challenges to traditional power systems caused by high variability of solar production, especially the ramp events, this paper is aimed at predicting solar radiation accurately at a very-short-term scale, i.e. several minutes ahead. Quite different from traditional methods, our designed system conducts time series prediction based upon meteorological data and sky images' features with the Long Short-Term Memory (LSTM) network to learn the long-term dependency. Experiments have been conducted based on sky images' feature extracted by Convolutional Neural Network, meteorological data and solar geometric data with a large number of features collected over a seven-summer period. Experimental results show that the proposed forecasting system outperforms other methods in the literature, such as solar forecasting based upon optical flow tracking, Feedforward Neural Network (FNN) and Support Vector Regression (SVR), in terms of accuracy and robustness.