A multi-scale computational model is proposed to calculate the mechanical responses of Fe-Cr-Al alloys with solid-solution and processing effects through a bidirectional coupling strategy. Based on crystal plasticity (CP) theory, a temperature-dependent critical resolved shear stress (CRSS) superposition model is constructed to couple with the molecular dynamics (MD), phase field model (PFM) and finite element method (FEM). By calibrating with few experimental data, we established an atom-informed solid solution strengthening model for multicomponent Fe-based alloys, thus successfully reproducing the polycrystalline features and stress-strain responses under different processing processes. Particularly, the multiscale model can provide high-precision yield strengths and reasonable tensile strength ranges for different grades of FeCrAl alloys. Finally, we present a case study employing an integration approach which starts from several experiment data, extends to hundreds of computational data and finally makes full-range prediction from artificial neural network methods. This study provides a viable and scalable scheme for the Materials Genome Initiative (MGI) design and optimization of nuclear-grade FeCrAl alloys.