A new retrieval algorithm for estimation of snow grain size and impurity concentration from spectral radiation data is developed for remote sensing applications. A radiative transfer (RT) model for the coupled atmosphere-snow system is used as a forward model. This model simulates spectral radiant quantities for visible and near-infrared channels. The forward RT calculation is, however, the most time-consuming part of the forward-inverse modeling. Therefore, we replaced it with a neural network (NN) function for fast computation of radiances and Jacobians. The retrieval scheme is based on an optimal estimation method with a priori constraints. The NN function was also employed to obtain an accurate first guess in the retrieval scheme. Validation with simulation data shows that a combination of NN techniques and optimal estimation method can provide more accurate retrievals than by using only NN techniques. In addition, validation with in-situ measurements conducted by using ground-based spectral radiometer system shows that comparison between retrieved snow parameters with in-situ measurements is acceptable with satisfactory accuracy. The algorithm provides simultaneous, accurate and fast retrieval of the snow properties. The algorithm presented here is useful for airborne/satellite remote sensing.