Air pollution is a pressing global challenge with severe consequences for human health and ecosystems, which underscores the need for accurate forecasting models. Traditional statistical and machine learning approaches frequently face difficulties in modeling the intricate and nonlinear patterns present in air pollution data. To overcome these limitations, this paper proposes the use of a modified Sinc neural network (MSNN) as a novel framework for time series forecasting of air pollution levels. The MSNN, inspired by Sinc numerical methods, leverages the smoothness and oscillatory properties of the Sinc function while incorporating a modification that enhances its ability to model nonlinear dependencies and temporal dynamics. A discrete-time Lyapunov-based online learning algorithm is employed to train the network, ensuring stability and convergence during parameter updates. The proposed model is evaluated on real-world datasets of air pollutants, including particulate matter ($PM_{10}$ and $PM_{2.5}$), sulfur dioxide, nitrogen monoxide, and ozone, collected from the city of Khorramabad, Iran. Comparative results demonstrate that, despite its simple structure, the MSNN achieves superior forecasting accuracy compared to conventional neural networks, highlighting its potential as an effective and computationally efficient tool for environmental time series prediction.