In this paper, we propose a new algorithm to improve the accuracy of the Wi-Fi access point (AP) positioning technique. The proposed algorithm based on evaluating the trustworthiness of the signal strength quality of each measurement node is superior to other existing AP positioning algorithms, such as the centroid, weighted centroid, multilateration, and radio distance ratio methods, owing to advantages such as reduction of distance errors during positioning, reduction of complexity, and ease of implementation. To validate the performance of the proposed algorithm, we conducted experiments in a complex indoor environment with multiple walls and obstacles, multiple office rooms, corridors, and lobby, and measured the corresponding AP signal strength value at several specific points based on their coordinates. Using the proposed algorithm, we can obtain more accurate positioning results of the APs for use in research or industrial applications, such as finding rogue APs, creating radio maps, or estimating the radio frequency propagation properties in an area.