This paper proposes an efficient feature extraction of the images by using independent component analysis(ICA) based on neural networks of the hybrid learning algorithm. The proposed learning algorithm is the fixed point(FP) algorithm based on Newton method and moment. The Newton method which uses to the tangent line for estimating the root of function, is applied for fast updating the inverse mixing matrix. The moment is also applied for getting the belter speed-up by restraining an oscillation due to compute the tangent line. The proposed algorithm has been applied to the 10,000 image patches of 12x12-pixel that are extracted from 13 natural images. The 144 features of 12x12―pixel and the 160 features of 16x 16-pixel have been extracted from all patches, respectively. The simulation results show that the extracted features have a localized characteristics being included in the images in space, as well as in frequency and orientation. And the proposed algorithm has better performances of the learning speed than those using the conventional FP algorithm based on Newton method.