A Einstein-Boltzmann system is the Einstein equations coupled with the Boltzmann equation, where the stress-energy tensor in the Einstein equations is described by the Boltzmann equation and the distribution function describing dynamics of relativistic gas determined by the Boltzmann equation is defined on the four dimensional manifold whose metric is given by the Einstein equation. In this talk, I'll discuss the existence and asymptotic behavior of solutions of the Einstein-Boltzmann system in spatially homogeneous space-time.