Growing metropolitan areas bring rapid urbanization and air pollution problems. As diseases and mortality rates increase because of the air pollution problem, it becomes a necessity to estimate the air pollution density and inform the public to protect the health. Air pollution problem displays contextual characteristics such as meteorological conditions, industrial and technological developments, traffic problem etc. that change from country to country and also from city to city. In this study, we determined PM10 as the target pollutant and designed a new deep learning based air quality forecasting model, namely DFS (Deep Flexible Sequential). Our study uses real world hourly data from Istanbul, Turkey between 2014 and 2018 to forecast the air pollution 4, 12, and 24 hours before. DFS model is a hybrid & flexible deep model including Long Short Term Memory (LSTM) and Convolutional Neural Network (CNN). The proposed model also is capable of generalization with standard and flexible Dropout layers. Through flexible Dropout layer, the model also obtains flexibility to adapt changing window sizes in sequential modelling. Moreover, this model can be applied to other air pollution time series data problems with small modifications on parameters by taking into account the nature of the data set.