Hyperspectral observations have become one of the most popular and powerful methods for atmospheric remote sensing, and are widely used for temperature, gas, aerosol, and cloud retrievals. However, accurate forward radiative transfer simulations are computationally expensive since typical line-by-line approaches involve a large number of monochromatic radiative transfer calculations. This study explores the feasibility of machine learning techniques (using neural network (NN) as an example) for fast hyperspectral radiative transfer simulations, by performing calculations at a small fraction of hyperspectral wavelengths and extending them across the entire spectral range. Results from the NN model are compared with those from a principal component analysis (PCA) model, which uses a similar principle of dimensionality reduction. We consider hyperspectral radiances from both actual satellite observations and accurate line-by-line simulations. The NN model can alleviate the computational burden by two to three orders of magnitude, and generate radiances with small relative errors (generally less than 0.5% compared to exact calculations); the performance of the NN model is better than that of the PCA model. The model can be further improved by optimizing the training procedure and parameters, the representative wavelengths, and the machine learning technique itself.