In the last decade, quantum computing (QC) has shown its great potential in advancing research in many fields. Here we introduce a new quantum-classical neural network, by combining quantum computing and classical computing in a hybrid neural network (HNN) that can be trained to perform image classification. The HNN on the basis of the classic convolutional neural network (CNN) with quantum circuit is considered for image classification problem. The various configurations of HNN were investigated where QC with different number of qubits were used and compared. The HNN configurations were trained, validated, and tested on the more complex CIFAR10 and CIFAR100 datasets in addition to our previous attempts on the simpler MNIST, notMNIST, MNIST Fashion datasets. Performance of HNN was compared for multiclass classification on these datasets for different number of classes (from 2 to 10) using QCs with correspondent number of qubits (from 2 to 4). The metrics measured (accuracy and loss) during these experiments support our assumption about feasibility of HNN application for multiclass classification problems.