The addition of dendritic inhibition has been shown to significantly enhance the computational and representational capabilities of neurons. However, this inhibitory mechanism is mostly ignored in existing artificial neural networks (ANNs). In this paper, we propose the alternating excitatory and inhibitory mechanisms and use them to construct an ANN-based dendritic neuron, the alternating excitation-inhibition dendritic neuron model (ADNM). Subsequently, a comprehensive multilayer neural system named the alternating excitation-inhibition dendritic neuron system (ADNS) is constructed by networking multiple ADNMs. To evaluate the performance of ADNS, a series of extensive experiments are implemented to compare it with other state-of-the- art networks on a diverse set consisting of 47 feature-based classification datasets and 2 image-based classification datasets. The experimental results demonstrate that ADNS outperforms its competitors in classification tasks. In addition, the impact of different hyper-parameters on the performance of the neural model is analyzed and discussed. In summary, the study provides a novel dendritic neuron model with better performance and interpretability for practical classification tasks.