The traditional reduced-form model (RFM) based on the high-order decoupled direct method (HDDM), is an efficient uncertainty analysis approach for air quality models, but it has large biases in uncertainty propagation due to the limitation of the HDDM in predicting nonlinear responses to large perturbations of model inputs. To overcome the limitation, a new stepwise-based RFM method that combines several sets of local sensitive coefficients under different conditions is proposed. Evaluations reveal that the new RFM improves the prediction of nonlinear responses. The new method is applied to quantify uncertainties in simulated PM concentrations in the Pearl River Delta (PRD) region of China as a case study. Results show that the average uncertainty range of hourly PM concentrations is -28% to 57%, which can cover approximately 70% of the observed PM concentrations, while the traditional RFM underestimates the upper bound of the uncertainty range by 1-6%. Using a variance-based method, the PM boundary conditions and primary PM emissions are found to be the two major uncertainty sources in PM simulations. The new RFM better quantifies the uncertainty range in model simulations and can be applied to improve applications that rely on uncertainty information.