We propose to train neural networks on top of support vector machine (SVM) classifiers learned from various visual features for efficiently classifying fingerprint images. Real datasets of fingerprint images are collected from students at the Can Tho University. The SVM algorithm learns classification models from the handcrafted features such as the scale-invariant feature transform (SIFT) and the bag-of-words (BoW) model, the histogram of oriented gradients (HoG), and the deep learning of invariant features (e.g., Inception-v3, Xception, VGG, ResNet50), extracted from fingerprint images. Followed which, neural networks are learned on top of SVM classifiers trained on these diverse visual features, making improvements of the fingerprint image classification. The empirical test results show that the proposed approach is more accurate than SVM classifiers trained on any single visual feature type. On average, a neural network trained on top of SVM-ResNet50, SVM-HoG, and SVM-SIFT-BoW improves 36.47, 12.30, and 8.74% classification accuracy against SVM-ResNet50, SVM-HoG, and SVM-SIFT-BoW, separately.