Linear dispersion properties and waves of collisionless plasma current sheet at small scales are discussed, using 25dimensional, collisionless and incompressible magnetohydrodynamic (MHD) models with the full electron pressure tensor. General dispersion relations are very complex. Two special cases, i.e., the central region of current sheet and the electronβ*e=0, are analytically studied here. The main results are as follows. (1) In the ioninertial region (kdi>1), there are fast magnetosonic-kinetic Alfven waves and obliquely Alfven-whistler waves, and the electron magnetohydrodynamic (EMHD) model is a precise MHD model. In the long wavelength region (kdi<1), there are Alfven waves and ion acoustic waves, and the ideal MHD model is valid. (2) When electron β*e=0, the results drop off some modes, e.g., the fast magnetosonic-kinetic Alfven wave and ion acoustic wave. This case is not exactly valid for the current sheet plasma. (3) At central region of current sheet, results from both of physical models have fast magnetosonic kinetic Alfven waves.