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Inspired by the works of Bridgeland and Gorsky on constructing Ringel-Hall algebras from Z/2-graded complexes, we consider the category C Z/2 (A) of Z/2-graded complexes over a hereditary abelian category A which may not have enough projective objects, and define the modified Ringel-Hall algebra of A, denoted by MH Z/2 (A), to be the localization of a quotient algebra of the Ringel-Hall algebra of C Z/2 (A). We prove such Ringel-Hall algebra to be of some nice properties and structures. The first one is that MH Z/2 (A) has a nice basis. As a consequence MH Z/2 (A) is a free module over a suitably defined quantum torus of acyclic complexes, with a basis given by the isomorphism classes of objects in the derived category of Z/2-graded complexes, and so in somehow MH Z/2 (A) has a similar meaning as the semi-derived Hall algebra of Gorsky. The second one is that in twisted case MH Z/2 (A) is isomorphic to the Drinfeld double Ringel-Hall algebra of H e tw (A), the twisted extended Ringel-Hall algebra of A itself. In particular, the category of finite-dimensional nilpotent representations of a quiver and the category of coherent sheaves on a smooth projective curve or on a weighted projective line are hereditary abelian categories, and so their twisted modified Ringel-Hall algebras are isomorphic to their Drinfeld double Ringel-Hall algebras. Finally, if A has a tilting object T , then its modified Ringel-Hall algebra is isomorphic to the Z/2-graded semi-derived Hall algebra SDH Z/2 (add T ) of the exact category add T defined by Gorsky and so isomorphic to the Bridgeland's Ringel-Hall algebra of mod(End(T )).

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