Magnetostriction of ferromagnetic materials describes the change of their shape or dimension in response to the reorientation of magnetization under the influence of external magnetic field. Fe(100-x)Ga(x) binary alloys (Galfenol) have large magnetostriction and excellent ductility; and they are very promising rare-earth free materials for applications in sensors, actuators, energy-harvesters and spintronic devices. Here we report results of large-scale ab initio molecular dynamics (AIMD) simulations for Galfenol, especially regarding the mechanism that leads to the sudden drop of tetragonal magnetostriction at x ~ 19, a long-standing puzzle for the community. Based on rigid band analysis, we propose possible ways to further optimize the performance of Galfenol for device applications. For example, we found that the substitution of a small amount of Cu for Ga (1.6%) in certain configuration may double the magnetostriction of Galfenol.