Chronic obstructive pulmonary disease (COPD) is a respiratory disorder involving abnormalities of lung parenchymal morphology with different severities. COPD is assessed by pulmonary-function tests and computed tomography-based approaches. We introduce a new classification method for COPD grouping based on deep learning and a parametric-response mapping (PRM) method. We extracted parenchymal functional variables of functional small airway disease percentage (fSAD%) and emphysema percentage (Emph%) with an image registration technique, being provided as input parameters of 3D convolutional neural network (CNN). The integrated 3D-CNN and PRM (3D-cPRM) achieved a classification accuracy of 89.3% and a sensitivity of 88.3% in five-fold cross-validation. The prediction accuracy of the proposed 3D-cPRM exceeded those of the 2D model and traditional 3D CNNs with the same neural network, and was comparable to that of 2D pretrained PRM models. We then applied a gradient-weighted class activation mapping (Grad-CAM) that highlights the key features in the CNN learning process. Most of the class-discriminative regions appeared in the upper and middle lobes of the lung, consistent with the regions of elevated fSAD% and Emph% in COPD subjects. The 3D-cPRM successfully represented the parenchymal abnormalities in COPD and matched the CT-based diagnosis of COPD.