Typical convolutional neural networks (CNNs) are widely used to recognize a user's stress state using the functional near-infrared spectroscopy (fNIRS), which is the latest brain imaging technology. fNIRS signals are usually fed into CNN models in the form of high-dimensional image data. However, this approach is not easy to achieve high classification accuracy because of physiological noises in brain signals. It is also likely to overlook the process of evaluating the reliability of calculated classification accuracy. To solve these problems, we proposed a memristor-based CNN (M-CNNs) This model's weight update process involves using stochastic gradient descent with momentum (SGDM), where the normalized conductances of memristors are used as weight substitutes. These conductances are then adjusted to classify stress states. We calculated the classification accuracies between the control and stress groups by using the M-CNNs, and then compared them with those of the CNNs. We used DenseNet, the most recent CNN model, to simulate accuracy under the same conditions. To ensure a fair comparison, we divided the DenseNet into the memristorbased DenseNet (M-DenseNet) and the conventional DenseNet (C-DenseNet). As a result, we discovered that the accuracy of M-CNNs (93.33%) exceeded that of CNNs (87.50%), and is reliable by precision, recall, and F-Score calculated from a confusion matrix. Likewise, M-DenseNet (92.38%) has higher accuracy than C-DenseNet (90.00%), but shows lower accuracy than M-CNNs. Moreover, we observed the reproducibility of M-CNN/DenseNet in various datasets. Therefore, our study suggests a promising application of CNN by combining conductances of memristor for classifying stress states.