The calculation of a model physics package in a typical moderate (a few degrees) resolution GCM like CAM-2 takes about 80% of the total model computations. The calculation of the long wave (LW) radiation takes about 70% of the time required for calculation of the model physics. In this work we apply neural network (NN) approximation technique to develop a fast and accurate approximation of a parameterization of the LW radiation. NN approximations of model physics are based on the fact that any parameterization of physics can be considered as a continuous or almost continuous mapping (input vector vs. output vector dependence), and NNs are a generic tool for fast and accurate approximation of such mappings. We evaluated the accuracy and performance of a NN approximation developed for the LW radiation parameterization in NCAR CAM. We selected the LW radiation as the mostly time consuming component of the model physics. Application of this approach allows accelerating calculation of LW radiation 65 times without compromising the accuracy of calculations. The systematic error introduced by the NN approximation is practically zero. The random error is very small and does not exceed several percents of the natural variability of the radiation parameters (about 0.05 K/day for heating rates and less than 1 Wt/m2 for the outgoing long wave radiation). Comparison of instantaneous heating rate profiles shows that the NN approximations are very close to the original profiles even for complicated cloudy profiles.