Mass spectrometry imaging (MSI) characterizes the molecular composition of tissues at spatial resolution, and has a strong potential for distinguishing tissue types, or disease states. This can be achieved by supervised classification, which takes as input MSI spectra, and assigns class labels to subtissue locations. Unfortunately, developing such classifiers is hindered by the limited availability of training sets with subtissue labels as the ground truth. Subtissue labeling is prohibitively expensive, and only rough annotations of the entire tissues are typically available. Classifiers trained on data with approximate labels have sub-optimal performance. To alleviate this challenge, we contribute a semi-supervised approach mi-CNN. mi-CNN implements multiple instance learning with a convolutional neural network (CNN). The multiple instance aspect enables weak supervision from tissue-level annotations when classifying subtissue locations. The convolutional architecture of the CNN captures contextual dependencies between the spectral features. Evaluations on simulated and experimental datasets demonstrated that mi-CNN improved the subtissue classification as compared to traditional classifiers. We propose mi-CNN as an important step toward accurate subtissue classification in MSI, enabling rapid distinction between tissue types and disease states. The data and code are available at https://github.com/Vitek-Lab/mi-CNN_MSI.