Quantum machine learning has been developing in recent years, demonstrating great potential in various research domains and promising applications for pattern recognition. However, due to the constraints of quantum hardware, the input qubits are restricted caused by small circuit size, and the fuzziness in all dimensions caused by the features that are difficult to be effectively mined. Besides, previous studies focus on binary classification, but multi-classification received little attention. To address the difficulty in multi-classification, this paper proposed a hybrid multi-branches quantum-classical neural network (HM-QCNN) that utilizes a multi-branch strategy to construct the convolutional part. The part consists of three branches to extract the features of different scales and morphologies. Two quantum convolutional layers apply quantum CRZ gates and rotational gates to design a random quantum circuit (RQC) with 4 qubits and full qubits measurements. The experiments on three public datasets (MNIST, Fashion MNIST, and MedMNIST) demonstrate that HM-QCNN outperforms other prevalent methods with accuracy, precision, and convergence speed. Compared with the classical CNN and the hybrid neural network without multi-branches, HM-QCNN reached 97.40% and improved the accuracy of classification by 6.45% and 1.36% on the MNIST dataset, respectively.