The abnormal behavior detection is the vital for evaluation of daily-life health status of the patient with cognitive impairment. Previous studies about abnormal behavior detection indicate that convolution neural network (CNN)-based computer vision owns the high robustness and accuracy for detection. However, executing CNN model on the cloud possible incurs a privacy disclosure problem during data transmission, and the high computation overhead makes difficult to execute the model on edge-end IoT devices with a well real-time performance. In this paper, we realize a skeleton-based abnormal behavior detection, and propose a secure partitioned CNN model (SP-CNN) to extract human skeleton keypoints and achieve safely collaborative computing by deploying different CNN model layers on the cloud and the IoT device. Because, the data outputted from the IoT device are processed by the several CNN layers instead of transmitting the sensitive video data, objectively it reduces the risk of privacy disclosure. Moreover, we also design an encryption method based on channel state information (CSI) to guarantee the sensitive data security. At last, we apply SP-CNN in abnormal behavior detection to evaluate its effectiveness. The experiment results illustrate that the efficiency of the abnormal behavior detection based on SP-CNN is at least 33.2% higher than the state-of-the-art methods, and its detection accuracy arrives to 97.54%.