The new parallel multiclass logistic regression algorithm (PAR-MC-LR) aims at classifying a very large number of images with very-high-dimensional signatures into many classes. We extend the two-class logistic regression algorithm (LR) in several ways to develop the new multiclass LR for efficiently classifying large image datasets into hundreds of classes. We propose the balanced batch stochastic gradient descend of logistic regression (BBatch-LR-SGD) for trainning two-class classifiers used in the one-versus-all strategy of the multiclass problems and the parallel training process of classifiers with several multi-core computers. The numerical test results on ImageNet datasets show that our algorithm is efficient compared to the state-of-the-art linear classifiers.