The concept of annihilator ideal is introduced in an almost distributive lattice with zero. It is observed that the set of all annihilator ideals of R forms a complete Boolean algebra, the sufficient condition for R to become a relatively complemented almost distributive lattice is derived. The concept of annihilator preserving homomorphism is introduced in R. A sufficient condition for a homomorphism to be annihilator preserving is derived. Finally, it is proved that the homomorphic images and the inverse images of an annihilator ideal are again annihilator ideals. Keywords: Almost Distributive Lattice, Boolean algebra, Annihilator ideal, relatively complemented Almost Distributive Lattice, annihilator preserving homomorphism.