Fast Fourier Transform ( FFT) method has been widely used in image recognition. However，FFTmethod faces some challenges，such as occlusion of different angles，varying lighting and changeable facial expression. We combine fast Fourier transform and feature space image representation method to solve the above problems. There are the following stages: ①Use FFT to extract spectral features from the original image. ②Use Gaussian kernel method to obtain new features in the feature space. The new features and the training samples of the original image use sparse representations to obtain sparse solutions. The new features and the test samples of original image can use the aforementioned sparse solution and its training samples to calculate scores respectively. Subsequently，the score and the new score can be used for image classification. This method has sparseness and robustness in image classification，and is very easy to implement. Experimental results show that the method proposed in this paper has high accuracy in image classification.