Acoustic scene classification (ASC) is a crucial research problem in computational auditory scene analysis, and it aims to recognize the unique acoustic characteristics of an environment. One of the challenges of the ASC task is the domain shift between training and testing data. Since 2018, ASC challenges have focused on the generalization of ASC models across different recording devices. Although this task, in recent years, has achieved substantial progress in device generalization, the challenge of domain shift between different geographical regions, involving discrepancies such as time, space, culture, and language, remains insufficiently explored at present. In addition, considering the abundance of unlabeled acoustic scene data in the real world, it is important to study the possible ways to utilize these unlabelled data. Therefore, we introduce the task Semi-supervised Acoustic Scene Classification under Domain Shift in the ICME 2024 Grand Challenge. We encourage participants to innovate with semi-supervised learning techniques, aiming to develop more robust ASC models under domain shift.