Deep learning is a powerful technique for data-driven learning in the era of Big Data. However, most deep learning models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to tackle this type of problem. In this article, we proposed a novel quantum assisted hierarchical fuzzy neural network (QA-HFNN). Different from classical fuzzy neural networks, QA-HFNN uses quantum neural networks (QNNs) to learn fuzzy membership functions. The model is a multifeature fusion learning algorithm with a parallel structural design that integrates quantum and classical neural networks. The classical network is used to capture high-dimensional neural features, the QNNs are designed to capture fuzzy logic features of the data, then, the two features are fused to form the final features to be classified. The experiment is performed on a classical computer, and the quantum circuit is built through a simulated quantum environment. The results indicate that the accuracy of QA-HFNN can equal to or even surpass classical methods in image classification tasks. The quantum circuit utilizes only a single qubit which is easy to implement. In addition, the fidelity of quantum circuit in a quantum noise environment is assessed, demonstrating that QA-HFNN has strong robustness. The time and computational complexity of QNNs was analyzed, further proving the effectiveness of the model.