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Abstract. The topic of duality on analysis has important role for developing some properties e.g. convergence. Köthe-Toeplitz dual for sequence is also important and has developed for many years. Chandra & Tripathy (2002) was introduced the notion h-dual as generalized Köthe-Toeplitz dual. In this paper we introduce the notion of some new double sequence spaces related with absolutely summable and bounded properties. We determined its h-dual. Also we verify the perfectness property of these new double sequence spaces relative to h-dual. We prove that its h-dual relate to summable double sequence space and bounded double sequence space.