Quantum vortices in Bose-Einstein condensates (BECs) are essential phenomena in condensed matter physics, and precisely locating their positions, especially the vortex core, is a prerequisite for studying their properties. With the rise of machine learning, there is a potential to expedite the localization process and provide accurate predictions. However, traditional machine learning requires a considerable amount of manual data annotation, leading to uncontrollable accuracy. In this paper, we utilize the U-Net method to detect vortex positions accurately at the pixel level and propose an Automatic Correction Labeling (ACL) approach to optimize the acquisition of data sets for vortex localization in BECs. This approach addresses inaccuracies in the labeled vortex positions and improves the accuracy of vortex localization, especially the vortex core positions, while enhancing the tolerance for human labeling. The main process involves Rough Labeling -- Machine Learning -- Probability Region Search -- Data Relabeling -- Machine Learning again. The objective of ACL is to obtain more accurate labeled data for model retraining. Through vortex localization experiments conducted in a two-dimensional Bose-Einstein condensate, our results demonstrate the following: 1. Even under conditions of biased and missing manual annotations, U-Net can still accurately locate vortex positions; 2. Vortices exhibit certain regularities, and training U-Net with a small number of samples yields excellent predictive results; 3. The machine learning vortex locator based on the iterative ACL method effectively corrects errors in manually annotated data, significantly improving the model's performance metrics, thus enhancing the precision and metrics of vortex localization. This substantial advancement in the application of machine learning in vortex localization provides an effective approach for vortex dynamics localization. Furthermore, this method of obtaining more accurate approximate human labels through machine learning offers new insights for machine learning in other types of image recognition problems.