Currently, human activity recognition (HAR) has been applied in many fields, including healthcare, smart homes, and sports tracking. The commonly-used LSTM-based methods have the disadvantage of having a relatively large number of parameters. This article proposes a HAR method based on a cascade architecture of deep feedforward sequential memory networks (DFSMN) and auxiliary classifier generative adversarial networks (ACGAN). In this research, a self-collected dataset was constructed through sampling data from inertial sensors worn by humans. DFSMN was used to extract temporal features from sensor data, and then in ACGAN, the extracted features were used to enhance the generator's ability to generate temporal data while using a discriminator for classification of activities. The model combining DFSMN with ACGAN can effectively improve the model's generalization ability and classification accuracy The experimental results indicate that this method can accurately recognize a wide range of human activities, such as walking, running, sitting, standing, going upstairs, going downstairs, and so on. This shows that the proposed method has a considerable application potential in practical scenarios.