Wi-Fi-based indoor positioning for determining accurate wireless indoor location information has become crucial in meeting increasing demands for location-based services by leveraging the Internet of Things (IoT) and ubiquitous connectivity. Most Wi-Fi-based indoor positioning techniques using wireless received signal strength (RSS)-based methods are affected by the indoor environment and depend on the respective signals from at least three reference access points. In this paper, we propose a cloudlet-based cloud computing system enabling Wi-Fi indoor positioning and navigation through a Wi-Fi located on a one-hop wireless network. Our cloudlet-based cloud computing system provides the reference point data and real-time interactive response for a self-driving indoor cart. The system was tested in a real environment with the following results: (1) our system autonomously performed actions, such as turning right or left or going straight according to a movement decision algorithm and determined the position within a stable range of Wi-Fi coverage; (2) the cloudlet and core cloud can track navigation for an indoor self-driving cart; (3) the global and local positions designed for reference access points and a specific position can navigate the self-driving cart to a particular position accurately; (4) the moving edge clouds play a role in deciding three action movements (go straight, turn left, and turn right), as well as managing the local position of the items; and (5) a core cloud is deployed to store all information for the items, such as their positions and corresponding Wi-Fi locations. A core cloud manages items that have the same position (i.e., a global position) defined as the corresponding Wi-Fi location. Finally, the practical results have significance in designing a cloudlet-based cloud computing system enabling Wi-Fi indoor positioning and navigation.