Recently, many attention-based deep neural networks have emerged and achieved state-of-the-art performance in environmental sound classification. The essence of attention mechanism is assigning contribution weights on different parts of features, namely channels, spectral or spatial contents, and temporal frames. In this paper, we propose an effective convolutional neural network structure with a multichannel temporal attention (MCTA) block, which applies a temporal attention mechanism within each channel of the embedded features to extract channel-wise relevant temporal information. This multi-channel temporal attention structure will result in a distinct attention vector for each channel, which enables the network to fully exploit the relevant temporal information in different channels. The datasets used to test our model include ESC-50 and its subset ESC-10, along with development sets of DCASE 2018 and 2019. In our experiments, MCTA performed better than the single-channel temporal attention model and the non-attention model with the same number of parameters. Furthermore, we compared our model with some successful attention-based models and obtained competitive results with a relatively lighter network.