Multi-object tracking (MOT) is one of the most challenging tasks in the field of computer vision. Although many MOT methods have been proposed in the literature, most of them cannot achieve real-time processing performance, especially those running on embedded platforms with limited computing resources. In this paper, we propose a real-time lightweight MOT method based on MobileNet to effectively improve the MOT processing speed. The proposed tracking method consists of a lightweight MOT model and a post-processing module. In the design of the lightweight MOT model, we have enhanced the lightweight object detection model proposed in our previous work by adding an appearance embedding layer. Moreover, we have also proposed a new anchor box design and a novel feature pyramid network (FPN) to improve the tracking accuracy of the proposed method. In the post-processing module, we have proposed a simple filtering method to replace the Kalman filter used in data association processing to accelerate the processing speed. Experimental results show that the proposed MOT method can reach to high processing speeds of 50.5 Frame-Per-Second (FPS) and 12.6 FPS when running on a desktop computer and an embedded platform, respectively. Moreover, the proposed MOT method also provides a competitive tracking performance when compared with the existing MOT methods. These advantages make the proposed method suitable for many applications running on embedded platforms, such as visual surveillance, visual tracking control of mobile robots, human-robot interaction, etc.