Abstract: Let \cal L = ( - \Delta )^2 + V^2 be a high order Schrödinger type operator in \rmR^n\;(n \geqslant 5), where V is a nonnegative potential satisfying the reverse Hölder inequality, and \cal V_\rho (\rme^ - t\cal L) be the variation operator associated with the high order Schrödinger type operator. Based on the theory of atomic decompesitions of Herz-Hardy spaces, using the properties of the Schrödinger type operators, the boundedness of the commutators composed by the variation operators associated with the Schrödinger type operators and BMO fuctions from Herz type Hardy spaces into the Herz spaces and the boundedness of the commutators on Morrey-Herz spaces are proved.