Over the last years convolutional neural networks (CNNs) have shown remarkable results in different image classification tasks, including medical imaging. One area that has been less explored with CNNs is Positron Emission Tomography (PET). Fluorodeoxyglucose Positron Emission Tomography (FDG-PET) is a PET technique employed to obtain a representation of brain metabolic function. In this study we employed 3D CNNs in FDG-PET brain images with the purpose of discriminating patients diagnosed with Parkinson's disease (PD) from controls. We employed Scaled Subprofile Modeling using Principal Component Analysis as a preprocessing step to focus on specific brain regions and limit the number of voxels that are used as input for the CNNs, thereby increasing the signal-to-noise ratio in our data. We performed hyperparameter optimization on three CNN architectures to estimate the classification accuracy of the networks on new data. The best performance that we obtained was accuracy = 0 . 8 6 and area under the receiver operating characteristic curve ( AUC ROC ) = 0 . 9 4 on the test set. We believe that, with larger datasets, PD patients could be reliably distinguished from controls by FDG-PET scans alone and that this technique could be applied to more clinically challenging tasks, like the differential diagnosis of neurological disorders with similar symptoms, such as PD, Progressive Supranuclear Palsy (PSP) and Multiple System Atrophy (MSA).