In recent years, environmental sound recognition has been effectively applied in embedded automatic audio classification devices and audio-based monitoring systems in smart cities. The development of convolutional neural networks (CNNs) has notably improved the accuracy of sound recognition. However, these models generally face a common issue: the feature extraction modules typically use CNNs and further employ convolutional or residual two-dimensional structures to extract and fuse high-level features based on low-level feature maps. This approach treats audio as if it were an image, overlooking the sequential characteristics inherent in audio data. In this context, this paper proposes a second-order recurrent neural network (RNN) method for environmental sound recognition. We extend the hidden layer calculations to relate not only to the previous time step but also to the two preceding time steps, thereby enhancing the aggregation of temporal information. Furthermore, for the classification module, we utilize a global attention module instead of the traditional fully connected network, achieving better accuracy.