Let A and B be two Banach algebras and let θ be a nonzero character on B.In this paper, we deal with the θ-Lau product A ×θ B that was first introduced by A. T. Lau for certain Banach algebras known as Lau algebras and recently by M. S. Monfared for all Banach algebras; we study pseudo-amenability, pseudo-contractibility and character pseudo-amenability of A×θ B and their relations with A and B.