In order to make the predictive simulation tools for the extracted beam current and emittance in the Linac4 H− ion source, we have launched the development of the integrated model for the H− ion beam formation and extraction process. More specifically, our 3D KEIO-Beam Formation and eXtraction (3D KEIO-BFX) is coupled with the NINJA, IBSIMU and TRAVEL. The extracted H− ion beam current and co-extracted electron current obtained by the integrated model have shown reasonable agreement with the experiments.