Abstract: This paper studies the local solvability of the differential equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is proved that for a class of inhomogeneous left invariant differential operators on the Heisenberg group,the local solvability of the corresponding equations is equivalent to the local sovability of the equations associated to their highest order terms.Then,under certain conditions on the highest order term,we obtain the necessary and sufficient conditions for the functon f to satisfy ill order for the differential equation Lu=f to be locally solvable.