Short-term demand forecasting for on-demand ride-hailing services is a fundamental issue in intelligent transportation systems. However, previous research predominantly focused on improving prediction accuracy, ignoring fairness issues such as systematic underestimations of travel demand in disadvantaged neighborhoods. This study investigates how to measure, evaluate, and enhance prediction fairness between disadvantaged and privileged communities in spatial-temporal demand forecasting of ride-hailing services. We developed a socially-aware neural network (SA-Net) that integrates socio-demographics and ridership information for fair demand prediction, and introduced a bias-mitigation regularization to reduce the prediction error gap between black and non-black, and low-income and high-income communities. The experimental results, using Chicago Transportation Network Company (TNC) data, demonstrate that our de-biasing SA-Net model outperforms other models in both prediction accuracy and fairness. Notably, the SA-Net exhibits a significant improvement in prediction accuracy, reducing 2.3% in Mean Absolute Error (MAE) compared to state-of-the-art models. When coupled with the bias-mitigation regularization, the de-biasing SA-Net effectively bridges the mean percentage prediction error (MPE) gap between the disadvantaged and privileged groups, and protects the disadvantaged regions against systematic underestimation of TNC demand. Specifically, our approach reduces the MPE gap between black and non-black communities by 67% without compromising overall prediction accuracy.