A Simultaneous Localization And Mapping (SLAM) system based on tightly coupled monocular Visual-Inertial-Encoder fusion and Oriented FAST and Rotated BRIEF (ORB) feature extraction, called SLAM-VIE-ORB, is proposed to solve the cost and security problems of intelligent elderly care robot. It aims at achieving localization accuracy high enough to ensure the safety of users - the elderly, while the cost is as low as possible to meet the needs of promotion in the field of intelligent elderly care robot service as the application of the most basic localization technology. Experiments under indoor and outdoor real environments on Qiming 2 robot using the proposed system comparing with the lidar-based adaptive Monte Carlo localization (AMCL) and VINS-Mono show that the localization error of SLAM-VIE-ORB is 80% of ACML and 50% of VINS-Mono, while the cost of the system is one fifth of AMCL which is used for traditional intelligent elderly care robot localization. The system for localization in the indoor static environment to help the elderly living alone will be put into use in the near future.