Abstract: In this paper the stochastic accelaration of ions in the plasma sheet boundary layer of the Earth's magnetotail by the broadband electrostatic noise is discussed. The calculations show that, due to the interaction with the noise, the trajectories of some ions in the phase space are stochastic. The area of the random motion in phase space is raleted to the amplitude, frequency and wave vector of the noise; through the stochastic accelaration, a part of the ions can be accelarated to the order of about 100 keV. These results may be used to explain the observations that some ions with very high energy exist in the plasma theet of the Earth magnetotail.