Let A be a δ-Koszul algebra, and let Ƙ( A) and L( A) denote the categories of δ-Koszul modules and modules with linear presentations. Some necessary and sufficient conditions for Ƙ( A) = L( A) are given. Set , where V is a minimal graded generating space of E( A). In the present paper, we prove that { B( A)| A is δ - Koszul} = ℕ. Finally, the Koszulity of the graded Hopf Galois extension of δ-Koszul algebras is studied.