A kinetic theory is developed to describe the longitudinal decay of two-ion decay (TID): The pump ion-acoustic wave (IAW) decays into two daughter IAWs with a longer wavelength. The instability growth rate and threshold are given by the theory. Both the simulations of full kinetic Vlasov and hybrid Vlasov (kinetic ions and Boltzmann electrons) are employed to verify the theory and have a high quantitative agreement with the theory for 8≤ZT_{e}/T_{i}≤15, where Z is the ion charge number and T_{i}(T_{e}) is the ion (electron) temperature. The kinetic model developed here solves a long-standing problem that the simple fluid theory underestimates growth rate by a factor of 2∼3. Also, a reasonable explanation is given to the typical characteristics of TID that the dependence curves of subharmonic growth rate γ and wave number k.