Abstract: In this paper we establish a set of kinetic equations from Liouville's theorem which can be used to describe the charged particle distribution in the accretion column of a neutron star.Abrief description of the general behavior of the plasma on a accretion column of a neutron star having a very strong magnetic field with a weak inhomoge-neity and with cylindrical symmetry is given.It is pointed out that the inhomogeneous magnetic field seems to have major effect on the plasma and the charged particle distribution in the accretion column greatly depend both on the magnetic field structure and on gravitational field of the neutron star.From the analysis we lead to the following conclusions.(1)The charged particle distribution in the accretion column with a very strong magnetic field is quite different from the one only controled by gravitational field of the neutron star as most of the high energy astrophysicists have done.Sometimes one would expect that the charged particles can be pushed outward along the direction of magnetic field and the matter density will increase with height.(2)Due to the difference in mass between the electron and the proton the distribution of protons with height is different from that of the electrons.So a strong electric field can take place near the surface of a neutron star.The type of electric field depends on the charged particle distribution.(3)For very young neutron stars,the role of the magnetic field may exceed that of the gravitational field.In this case there will be no possibility to form the accretion column and the pulse radiation therefore can not be produced.