We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${alpha},{eta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${alpha},{eta}$)-metrics be weakly-Berwald spaces, respectively.