In this paper, we introduce and investigate the notion of almost contra-g-continuous functions which is weaker than both notions of contra-continuous functions [Dontchev J. Contra-continuous functions and strongly S-closed mappings. Int J Math Math Sci 1996;19:303-10] and (θ, s)-continuous functions [Joseph JK, Kwak MK. On S-closed spaces. Proc Am Math Soc 1980;80:341-8.] in topological spaces. We discuss the relationships with some other related functions. At the same time, we show that almost-g-continuity and (LC, s)-continuity are independent of each other. Crown Copyright © 2008.