Image recognition and classification are fundamental tasks with diverse practical applications across various industries, making them critical in the modern world. Recently, machine learning models, particularly neural networks, have emerged as powerful tools for solving these problems. However, the utilization of quantum effects through hybrid quantum-classical approaches can further enhance the capabilities of traditional classical models. Here, we propose two hybrid quantum-classical models: a neural network with parallel quantum layers and a neural network with a quanvolutional layer, which address image classification problems. One of our hybrid quantum approaches demonstrates remarkable accuracy of more than 99% on the MNIST dataset. Notably, in the proposed quantum circuits all variational parameters are trainable, and we divide the quantum part into multiple parallel variational quantum circuits for efficient neural network learning. In summary, our study contributes to the ongoing research on improving image recognition and classification using quantum machine learning techniques. Our results provide promising evidence for the potential of hybrid quantum-classical models to further advance these tasks in various fields, including healthcare, security, and marketing.