We propose a new learning algorithm of latent local support vector machines (SVM), called Latent-lSVM for effectively classifying very-high-dimensional and large-scale multi-class image datasets. The common framework of image classification tasks using the Scale-Invariant Feature Transform method (SIFT) and the Bag-of-visual-Words (BoW), leads to hard classification problem with thousands of dimensions and hundreds of classes. Our Latent-lSVM algorithm performs these complex tasks into two main steps. The first one is to use latent Dirichlet allocation (LDA) for assigning the image to some topics (clusters) with the corresponding probabilities. This aim is to reduce the number of classes and the number of datapoints in the cluster compared to the full dataset, followed by the second one: to learn a SVM model for each cluster to non-linearly classify the data locally. The numerical test results on eight real datasets show that the Latent-lSVM algorithm achieves very high accuracy compared to state-of-the-art algorithms. An example of its effectiveness is given with an accuracy of 97.87\% obtained in the classification of fingerprint dataset having 5000 dimensions into 559 classes.