Abstract : Local cohomology is an important tool for commutative algebraist’s. However except in the case of the maximal ideal, the local cohomology modules are poorly understood. Let R = k[X1, . . . , Xn] where k is a field of characteristic zero. We show that local cohomology modules over R are finitely generated modules over the n th-Weyl algebra, An(K). Note that An(K) is a simple non-commutative domain. Properties of Weyl-algebra forces some properties on local cohomology modules over R as well.