In this paper we introduce approximate φ-biprojective Banach algebras, where φ is a non-zero character. We show that for SIN group G, the group algebra L 1 (G) is approximately φ-biprojective if and only if G is amenable, where φ is the augmentation character. Also we show that the Fourier algebra A(G) over a locally compact G is always approximately φ-biprojective
