Ultrasound localization microscopy (ULM) has been developed to significantly improve the spatial resolution of ultrasound imaging by localizing the microbubbles (MBs). However, owing to the unsatisfactory performance of conventional localization methods in localizing overlapped MBs, low MB concentration is typically required, which leads to a long data-acquisition time. Recently, deep learning (DL)-based localization methods have been proposed to improve the precision and processing speed of localization at high MB concentrations. Because the ground truth of in vivo MB locations is difficult to obtain, labeled training datasets are usually generated by simulations. Considering the differences between the simulated and experimental data, the performance of the trained convolutional neural network (CNN) may not generalize well on experimental data. In this study, a self-supervised learning scheme is proposed to train the CNN directly using experimental data and is evaluated on ex vivo chicken embryo chorioallantoic membrane (CAM) data at high MB concentration. Conventional cross-correlation (CC)-based localization method is used for comparison, and the results show that the proposed method performs much better in localization of high-concentration MBs than the CC-based method. In addition, the proposed method forms a closed loop for neural network training through experimental data and bypasses the requirement for labeled training dataset, which is typically generated using simulations.