Proactively detecting falls and preventing injuries are among the primary keys to a healthy life for the elderly. Near-fall remote monitoring in daily life could provide key information to prevent future falls and obtain quantitative rehabilitation status for patients with weak balance ability. In this study, we developed a deep learning-based novel classification algorithm to precisely categorize three classes (falls, near-falls, and activities of daily living (ADLs)) using a single inertial measurement unit (IMU) device attached to the waist. A total of 34 young participants were included in this study. An IMU containing accelerometer and gyroscope sensors was fabricated to acquire acceleration and angular velocity signals. A comprehensive experiment including thirty-six types of activities (10 types of falls, 10 types of near-falls, and 16 types of ADLs) was designed based on previous studies. A modified directed acyclic graph-convolution neural network (DAG-CNN) architecture with hyperparameter optimization was proposed to predict fall, near-fall, and ADLs. Prediction results of the modified DAG-CNN structure were found to be approximately 7% more accurate than the traditional CNN structure. For the case of near-falls, the modified DAG-CNN demonstrated excellent prediction performance with accuracy of over 98% by combining gyroscope and accelerometer features. Additionally, by combining acceleration and angular velocity the trained model showed better performance than each model of acceleration and angular velocity. It is believed that information to preemptively handle the risk of falls and quantitatively evaluate the rehabilitation status of the elderly with weak balance will be provided by monitoring near-falls.