We propose a new parallel learning algorithm of latent local support vector machines (SVM), called latent-lSVM for effectively classifying very high-dimensional and large-scale multi-class datasets. The common framework of texts/images classification tasks using the Bag-Of-(visual)-Words model for the data representation 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 for assigning the datapoint (text/image) to some topics (clusters) with the corresponding probabilities. This aims at reducing the number of classes and the number of datapoints in the cluster compared to the full dataset, followed by the second one: to learn in a parallel way nonlinear SVM models to classify data clusters locally. The numerical test results on nine 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 70.14% obtained in the classification of Book dataset having 100 000 individuals in 89 821 dimensional input space and 661 classes in 11.2 minutes using a PC Intel(R) Core i7-4790 CPU, 3.6 GHz, 4 cores.