Improving health equity is an urgent task for our society. The advent of mobile clinics plays an important role in enhancing health equity, as they can provide easier access to preventive healthcare for patients from disadvantaged populations. For effective functioning of mobile clinics, accurate prediction of demand (expected number of individuals visiting mobile clinic) is the key to their daily operations and staff/resource allocation. Despite its importance, there have been very limited studies on predicting demand of mobile clinics. To the best of our knowledge, we are among the first to explore this area, using AI-based techniques. A crucial challenge in this task is that there are no known existing data sources from which we can extract useful information to account for the exogenous factors that may affect the demand, while considering protection of client privacy. We propose a novel methodology that completely uses public data sources to extract the features, with several new components that are designed to improve the prediction. Empirical evaluation on a real-world dataset from the mobile clinic The Family Van shows that, by leveraging publicly available data (which introduces no extra monetary cost to the mobile clinics), our AI-based method achieves 26.4% - 51.8% lower Root Mean Squared Error (RMSE) than the historical average-based estimation (which is presently employed by mobile clinics like The Family Van). Our algorithm makes it possible for mobile clinics to plan proactively, rather than reactively, as what has been doing.