Criterion of the Jeans modes for self-gravitational systems in Eddington-inspired Born-Infeld (EiBI) gravity is revisited based on the framework of nonextensive statistics and kinetic theory. The results show the nonextensive parameter q has significant effects on the growth rate and critical wave-number of Jeans instability for the EiBI-gravitational systems. Also, we prove that the standard dispersion relationship proposed by Binney can be recovered if q→1 and τ→0. Concept of Jeans critical value (that is, the Jeans thresholds of EiBI gravitational systems) obtains a more tight emendation and the results of present work may provide theoretical references for the evolution of stars such as neutron stars, accretion disks, and relevant plasma physics, etc.