In this paper, we investigate left φ-biprojectivity of Segal algebras and abstract Segal algebras. We show that for some abstract Segal algebras with some mild conditions left φ-biprojectivity is equivalent with left φ-contractibility. Also we characterize left φbiprojectivity of a Segal algebra S(G) in the terms of compactness of G, where G is a locally compact group. We introduce a class of abstract Segal algebras among Triangular Banach algebras. We show that some abstract Segal algebras related to triangular Banach algebras are not biprojective
