Dementia is a neurodegenerative disease with a high incidence in the elderly. However, there is no effective treatment for this disease, and early intervention has a great effect to slow the deterioration. Currently, the detection of dementia is mainly achieved using questionnaire-like neuropsychological tests. Such ways usually cost a lot of time. To this end, we design a contactless dementia detection system based on gait analysis from surveillance video, and it can serve as a home-based healthcare system. This system applies a Kinect 2.0 camera to capture the human video and extract the skeleton joints at a rate of 15 frames per second. Two different gaits are collected for detection, namely single-task gait and dual-task gait. In this paper, we design a convolutional neural network based classifier to extract features in a data-driven way from these two groups of videos, but not take hand-crafted features. Experimental results show that we achieve a sensitivity of 74.10% on the test set using this system, and the processing only takes several minutes for early dementia detection.