The influence of the κ-deformed Kaniadakis distribution on Jeans instability in the background of f(R) gravity is investigated, the dispersion relation considering the κ-deformed Kaniadakis distribution is derived by exploiting the kinetic theory. The cases of high and low frequency perturbations are analyzed, respectively, it is found that the range of the unstable modes and the growth rates decrease with the increased distribution index κ in both of high and low frequency regime. Finally, based on the derivation of effective temperature, the relation between Jeans mass and temperature is studied, it is found that lower Jeans mass means that the system is more likely to collapse due to gravitational instability, the system is unstable for lower distribution index κ.