We systematically investigated the influence of strain on the electronic structure and ferromagnetism of (In,Fe)As thin films. It is found that while the shift of the critical point energies of compressive-strained (In,Fe)As layers grown on (In1-y,Ga-y)As (y = 0.05, 0.1) buffer layers can be explained by the hydrostatic deformation effect (HDE) alone, those of tensile-strained (In,Fe)As layers grown on (Ga1-z,Al-z)Sb (z = 0, 0.5, 1) buffer layers can be explained by the combination of HDE and the quantum confinement effect (QCE). The Curie temperature T-C of the (In, Fe)As layers strongly depends on the strain, and shows a maximum for the (In,Fe)As layer grown on a GaSb buffer layer. The strain dependence of T-C can be explained by the s-d exchange mechanism taking into account HDE and QCE. (C) 2014 AIP Publishing LLC.