The precise detection of falls is essential for promptly providing first aid to individuals who are at risk of accidental injury. Presently, the predominant approach for detecting falls is through inertial measurement unit (IMU) sensors, which can capture the real-time motion of an object. However, it is difficult for the current approach to face the challenges in attaining the anticipated performance in real-world applications, owing to the diverse nature of human behavior. To tackle this concern, a fall detection approach that uses a graph convolutional neural network (GCN) with variable time windows (T-GCN) is introduced. The proposed method uses well-designed graph topologies to effectively mitigate the impact of inconsistent data dimensions. Meanwhile, variable time windows are designed to capture keyframe data and to enhance their validity. To evaluate the effectiveness of the T-GCN method, a dataset Dhard containing 12 suspected falls and four real falls is built. The experimental results show that the T-GCN method achieves an accuracy of 91.3% and a precision of 92.5%, surpassing the average accuracy and precision of conventional fall detection methods.