Over the past few years, the concentration of fine particulate matter (PM2.5) in Delhi's atmosphere has progressively increased, resulting in smog episodes and affecting people's health. Therefore, accurate and reliable forecasting of PM2.5 concentration is essential to guide effective precautions before and during extreme pollution events. In this work, soft computing techniques, including Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) are employed to predict PM2.5 concentrations in Delhi. Four models, namely, multi-layer feedforward neural network (MLFFNN), General regression neural network (GRNN), Gaussian progression regression with ARD squared exponential kernel(GPARD_sqexp) and Gaussian progression regression with ARD rational quadratic kernel (GPARD_rat_quad) are built using meteorological and air quality data corresponding to a two-year period (2015)(2016). The results of the study suggested that MLFFNN showed the best prediction performance among the four models, with testing correlation coefficient (R) 0.949, Root mean square error (RMSE) 30.193, Nash-Sutcliffe efficiency index (NSE) 0.892 and Mean absolute error (MAE) 18.388. Moreover, sensitivity analysis performed to understand the importance of different input variables reported that PM10, wind speed, AQI and Z0 are the most critical parameters influencing MLFFNN model forecasts. On the whole, the work has demonstrated that the artificial neural network model is more capable of dealing with PM2.5 forecasting in Delhi urban area than the Gaussian process regression model.