Spectral photoacoustic imaging (sPAI) is an emerging modality that allows real-time, non-invasive, and radiation-free assessment of tissue, benefiting from their optical contrast. sPAI is ideal for morphology assessment in arterial plaques, where plaque composition provides relevant information on plaque progression and its vulnerability. However, since sPAI is affected by spectral coloring, general spectroscopy unmixing techniques cannot provide reliable identification of such complicated sample composition. In this study, we employ a convolutional neural network (CNN) for the classification of plaque composition using sPAI. For this study, nine carotid endarterectomy plaques were imaged and were then annotated and validated using multiple histological staining. Our results show that a CNN can effectively differentiate constituent regions within plaques without requiring fluence or spectra correction, with the potential to eventually support vulnerability assessment in plaques.