Artificial Intelligence (AI) and machine learning have been increasingly adopted for forecasting real-time travel demand. These AI-based travel demand forecasting models, though generate highly-accurate predictions, may produce prediction biases and thus raise fairness issues. Using such models for decision-making, we may develop transportation policies that could exacerbate social inequalities. However, limited studies have been focused on addressing the fairness issues of AI-based travel demand forecasting models. Therefore, in this study, we propose a novel methodology to develop fairness-aware travel demand forecasting models, which are highly accurate and fair. Specifically, we add a fairness regularization term, i.e., the correlation between prediction accuracy and the protected attribute such as race or income, into the loss function of the travel demand forecasting model. We include an interactive weight coefficient to both accuracy loss term and fairness loss term. The travel demand forecasting models can thus simultaneously account for prediction accuracy and fairness. An empirical analysis is conducted using real-world ridesourcing-trip data in Chicago. Results show that our proposed methodology effectively addresses the accuracy-fairness trade-off. It can significantly enhance fairness for multiple protected attributes (i.e., race, education, age and income) by only sacrificing a small accuracy drop. This study provides transportation professionals a new type of decision-support tool to achieve fair and accurate travel demand forecasting.