We study matrix type actions of finite abelian groups on simple higher dimensional noncommutative tori. For a given dimension d and a finite abelian group G, we apply a certain function to detect whether there is a simple noncommutative d-torus which admits such an action of G. For possible cases, we construct all such actions of G, and compute the K-theory of the resulting crossed products. We also give a necessary and sufficient condition of G under which the resulting crossed product is an AF algebra.