Imaging mass spectrometry (IMS) is a novel molecular imaging technique to investigate how molecules are distributed between tumors and within tumor region in order to shed light into tumor biology or find potential biomarkers. Convolutional neural networks (CNNs) have proven to be very potent classifiers often outperforming other machine learning algorithms, especially in computational pathology. To overcome the challenge of complexity and high-dimensionality of the IMS data, the proposed CNNs are either very deep or use large kernels, which results in large amount of parameters and therefore a high computational complexity. An alternative is down-sampling the data, which inherently leads to a loss of information. In this paper, we propose using dilated CNNs as a possible solution to this challenge, since it allows for an increase of the receptive field size, neither by increasing the network parameters nor by decreasing the input signal resolution. Since the mass signature of cancer biomarkers are distributed over the whole mass spectrum, both locally- and globally-distributed patterns need to be captured to correctly classify the spectrum. By experiment, we show that employing dilated convolutions in the architecture of a CNN leads to a higher performance in tumor classification. Our proposed model outperforms the state-of-the-art for tumor classification in both clinical lung and bladder datasets by 1-3%.