Abstract: The Invariant Subspace Problem is a famous problem in the operator theory.For generalizing the results in Abramovich's paper about the positive compact operators,this paper is devoted to the properties of AM-compact operators on Banach lattice.Its domination and lattice property is given,and it is proven that if a positive operator on a Banach lattice is dominated by an AM-compact operator,then its square is also an AM-compact operator.Some relative properties are also discussed.