Skeleton-based action recognition has become popular in recent years due to its efficiency and robustness. Most current methods adopt graph convolutional network (GCN) for topology modeling, but GCN-based methods are limited in long-distance correlation modeling and generalizability. In contrast, the potential of convolutional neural network (CNN) for topology modeling has not been fully explored. In this paper, we propose a novel CNN architecture, Temporal-Channel Topology Enhanced Network (TCTE-Net), to learn spatial and temporal topologies for skeleton-based action recognition. The TCTE-Net consists of two modules: the Temporal-Channel Focus module, which learns a temporal-channel focus matrix to identify the most important feature representations, and the Dynamic Channel Topology Attention module, which dynamically learns spatial topological features, and fuses them with an attention mechanism to model long-distance channel-wise topology. We conduct experiments on NTU RGB+D, NTU RGB+D 120, and FineGym datasets. TCTE-Net shows state-of-the-art performance compared to CNN-based methods and achieves superior performance compared to GCN-based methods. The code is available at https://github.com/aikuniverse/TCTE-Net.