In this paper, we proposed a robust music genre classification method based on a sparse FFT based feature extraction method which extracted with discriminating power of spectral analysis of non-stationary audio signals, and the capability of sparse representation based classifiers. Feature extraction method combines two sets of features namely short-term features (extracted from windowed signals) and long-term features (extracted from combination of extracted short-time features). Experimental results demonstrate that the proposed feature extraction method leads to a sparse representation of audio signals. As a result, a significant reduction in the dimensionality of the signals is achieved. The extracted features are then fed into a sparse representation based classifier (SRC). Our experimental results on the GTZAN database demonstrate that the proposed method outperforms the other state of the art SRC approaches. Moreover, the computational efficiency of the proposed method is better than that of the other Compressive Sampling (CS)-based classifiers.