In this study, we developed a $PM_{10}$ forecasting model using DNN and Membership Function, and improved the forecasting performance. The model predicts the $PM_{10}$ concentrations of the next 3 days in the Seoul area by using the weather and air quality observation data and forecast data. The best model(RM14)'s accuracy (82%, 76%, 69%) and false alarm rate(FAR:14%,33%,44%) are good. Probability of detection (POD: 79%, 50%, 53%), however, are not good performance. These are due to the lack of training data for high concentration $PM_{10}$ compared to low concentration. In addition, the model dose not reflect seasonal factors closely related to the generation of high concentration $PM_{10}$. To improve this, we propose Julian date membership function as inputs of the $PM_{10}$ forecasting model. The function express a given date in 12 factors to reflect seasonal characteristics closely related to high concentration $PM_{10}$. As a result, the accuracy (79%, 70%, 66%) and FAR (24%, 48%, 46%) are slightly reduced in performance, but the POD (79%, 75%, 71%) are up to 25% improved compared with those of the RM14 model. Hence, this shows that the proposed Julian forecast model is effective for high concentration $PM_{10}$ forecasts.