The traditional space-time adaptive processing (STAP) methods require large training samples to estimate the clutter covariance matrix. Sparse recovery STAP (SR-STAP) can get a highly accurate estimation in the case of insufficient samples and it alleviates the above problem of conventional STAP methods, however, the price of SR-STAP is that it involves a huge computational load in optimization, especially when the input data size is very big. This paper proposed a novel SR-STAP dictionary construction method that can significantly improve computational efficiency. We introduce the noise grids as the supplement of the spectrum-aid methods and design a second grids screening method based on the prior spectrum information. After the process of the proposed method, the dimension of the space-time dictionary has a sharp decrease compared to the over-complete dictionary, moreover, the sparsity of variable can be maintained better than the common spectrum-aid methods. The numerical experiments verify that the proposed method not only can significantly reduce the optimization time to far smaller than the SR-STAP but also more robust than spectrum-aid methods even in the small input size.