Multi-parametric magnetic resonance imaging (mpMRI) exams have various series types acquired with different imaging protocols. The DICOM headers of these series often have incorrect information due to the sheer diversity of protocols and occasional technologist errors. To address this, we present a deep learning-based classification model to classify 8 different body mpMRI series types so that radiologists read the exams efficiently. Using mpMRI data from various institutions, multiple deep learning-based classifiers of ResNet, EfficientNet, and DenseNet are trained to classify 8 different MRI series, and their performance is compared. Then, the best-performing classifier is identified, and its classification capability under the setting of different training data quantities is studied. Also, the model is evaluated on the out-of-training-distribution datasets. Moreover, the model is trained using mpMRI exams obtained from different scanners in two training strategies, and its performance is tested. Experimental results show that the DenseNet-121 model achieves the highest F1-score and accuracy of 0.966 and 0.972 over the other classification models with p-value$<$0.05. The model shows greater than 0.95 accuracy when trained with over 729 studies of the training data, whose performance improves as the training data quantities grew larger. On the external data with the DLDS and CPTAC-UCEC datasets, the model yields 0.872 and 0.810 accuracy for each. These results indicate that in both the internal and external datasets, the DenseNet-121 model attains high accuracy for the task of classifying 8 body MRI series types.