In this paper, we introduce an emerging quantum machine learning (QML) framework to assist classical deep learning methods for biosignal processing applications. Specifically, we propose a hybrid quantum-classical neural network model that integrates a variational quantum circuit (VQC) into a deep neural network (DNN) for electroencephalogram (EEG), electromyogram (EMG), and electrocorticogram (ECoG) analysis. We demonstrate that the proposed quantum neural network (QNN) achieves state-of-the-art performance while the number of trainable parameters is kept small for VQC.