Rapid and accurate clinical diagnosis remains challenging. A component of diagnosis tool development is the design of effective classification models with Mass spectrometry (MS) data. Some Machine Learning approaches have been investigated but these models require time-consuming preprocessing steps to remove artifacts, making them unsuitable for rapid analysis. Convolutional Neural Networks (CNNs) have been found to perform well under such circumstances since they can learn representations from raw data. However, their effectiveness decreases when the number of available training samples is small, which is a common situation in medicine. In this work, we investigate transfer learning on 1D-CNNs, then we develop a cumulative learning method when transfer learning is not powerful enough. We propose to train the same model through several classification tasks over various small datasets to accumulate knowledge in the resulting representation. By using rat brain as the initial training dataset, a cumulative learning approach can have a classification accuracy exceeding 98% for 1D clinical MS-data. We show the use of cumulative learning using datasets generated in different biological contexts, on different organisms, and acquired by different instruments. Here we show a promising strategy for improving MS data classification accuracy when only small numbers of samples are available.