Healthcare using body sensor data has been getting huge research attentions by a wide range of researchers because of its good practical applications such as smart health care systems. For instance, smart wearable sensor-based behavior recognition system can observe elderly people in a smart eldercare environment to improve their lifestyle and can also help them by warning about forthcoming unprecedented events such as falls or other health risk, to prolong their independent life. Although there are many ways of using distinguished sensors to observe behavior of people, wearable sensors mostly provide reliable data in this regard to monitor the individual’s functionality and lifestyle. In this paper, we propose a body sensor-based activity modeling and recognition system using time-sequential information-based deep Neural Structured Learning (NSL), a promising deep learning algorithm. First, we obtain data from multiple wearable sensors while the subjects conduct several daily activities. Once the data is collected, the time-sequential information then go through some statistical feature processing. Furthermore, kernel-based discriminant analysis (KDA) is applied to see the better clustering of the features from different activity classes by minimizing inner-class scatterings while maximizing inter-class scatterings of the samples. The robust time-sequential features are then applied with Neural Structured Learning (NSL) based on Long Short-Term Memory (LSTM), for activity modeling. The proposed approach achieved around 99% recall rate on a public dataset. It is also compared to existing different conventional machine learning methods such as typical Deep Belief Network (DBN), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN) where they yielded the maximum recall rate of 94%. Furthermore, a fast and efficient explainable Artificial Intelligence (XAI) algorithm, Local Interpretable Model-Agnostic Explanations (LIME) is used to explain and check the machine learning decisions. The robust activity recognition system can be adopted for understanding peoples' behavior in their daily life in different environments such as homes, clinics, and offices.