Radar-based human activity recognition (HAR) provides a non-contact method for many scenarios, such as human-computer interaction, smart security, and advanced surveillance with privacy protection. Feeding radar-preprocessed micro-Doppler signals into a deep learning (DL) network is a promising approach for HAR. Conventional DL algorithms can achieve high performance in terms of accuracy, but the complex network structure causes difficulty for their real-time embedded application. In this study, an efficient network with an attention mechanism is proposed. This network decouples the Doppler and temporal features of radar preprocessed signals according to the feature representation of human activity in the time-frequency domain. The Doppler feature representation is obtained in sequence using the one-dimensional convolutional neural network (1D CNN) following the sliding window. Then, HAR is realized by inputting the Doppler features into the attention-mechanism-based long short-term memory (LSTM) as a time sequence. Moreover, the activity features are effectively enhanced using the averaged cancellation method, which improves the clutter suppression effect under the micro-motion conditions. Compared with the traditional moving target indicator (MTI), the recognition accuracy is improved by about 3.7%. Experiments based on two human activity datasets confirm the superiority of our method compared to traditional methods in terms of expressiveness and computational efficiency. Specifically, our method achieves an accuracy close to 96.9% on both datasets and has a more lightweight network structure compared to algorithms with similar recognition accuracy. The method proposed in this article has great potential for real-time embedded applications of HAR.