In this project we define skew Heyting almost distributive lattice and characterize it as a skew Heyting algebra in terms of congruence relation defined on it. Moreover, we also present different conditions on which an ADL with maximal element m becomes skew HADL and a skew HADL to become skew Heyting algebra. We define an equivalence relation θ on a skew HADL and prove that θ is a congruence relation on the equivalence class[𝑥]𝜃. So we generalized that each congruence class is a maximal rectangular sub-algebra. Further in order to clarify more, we give three examples that verify skew HADL. The achieved properties reveal that skew HADL generalizes skew Heyting algebra. Finally, we prove different theorems, corollaries and lemmas related to skew HADL.