The conventional dendritic neuron model (DNM) is a single-neuron model inspired by biological dendritic neurons that has been applied successfully in various fields. However, an increasing number of input features results in inefficient learning and gradient vanishing problems in the DNM. Thus, the DNM struggles to handle more complex tasks, including multiclass classification and multivariate time-series forecasting problems. In this study, we extended the conventional DNM to overcome these limitations. In the proposed dendritic neural network (DNN), the flexibility of both synapses and dendritic branches is considered and formulated, which can improve the model's nonlinear capabilities on high-dimensional problems. Then, multiple output layers are stacked to accommodate the various loss functions of complex tasks, and a dropout mechanism is implemented to realize a better balance between the underfitting and overfitting problems, which enhances the network's generalizability. The performance and computational efficiency of the proposed DNN compared to state-of-theart machine learning algorithms were verified on 10 multiclass classification and 2 high-dimensional binary classification datasets. The experimental results demonstrate that the proposed DNN is a promising and practical neural network architecture.