Computing devices that can recognize various human activities or movements can be used to assist people in healthcare, sports, or human-robot interaction. Readily available data for this purpose can be obtained from the accelerometer and the gyroscope built into everyday smartphones. Effective classification of real-time activity data is, therefore, actively pursued using various machine learning methods. In this study, the transformer model, a deep learning neural network model developed primarily for the natural language processing and vision tasks, was adapted for a time-series analysis of motion signals. The self-attention mechanism inherent in the transformer, which expresses individual dependencies between signal values within a time series, can match the performance of state-of-the-art convolutional neural networks with long short-term memory. The performance of the proposed adapted transformer method was tested on the largest available public dataset of smartphone motion sensor data covering a wide range of activities, and obtained an average identification accuracy of 99.2% as compared with 89.67% achieved on the same data by a conventional machine learning method. The results suggest the expected future relevance of the transformer model for human activity recognition.