The report presents an algorithm for constructing a convolutional hierarchical neural network classifier, which is a modification of the algorithm for constructing hierarchical neural network classifiers suggested before. The original algorithm was designed to exploit intrinsic class hierarchy to build a class tree with a neural network in each node classifying groups of initial classes (in a non-terminal node) or a subset of original classes (in a terminal node). The convolutional modification utilizes convolutional neural networks instead of regular fully connected networks in order to apply the model to image classification tasks. Use of class hierarchy for image classification should reduce the number of adjusted neural network parameters compared to deep convolutional neural networks, and therefore it should reduce training and inference time. In this context the algorithm may be compared with some pruning techniques. The convolutional hierarchical neural network classifier inherits some hyperparameters of a conventional hierarchical neural network classifier, like the activation threshold and the threshold by the share of voting patterns. The goal of this study was to explore different strategies of choosing these hyperparameters. To test these strategies, we used the CIFAR-10 dataset. Also, for demonstration purposes we apply the convolutional hierarchical neural network classifier to the CIFAR-100 dataset.