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This paper focuses on designing a tweakable block cipher via by tweaking the Key-Alternating Feistel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">KAF</mi></semantics></math></inline-formula> for short) construction. Very recently Yan et al. published a tweakable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">KAF</mi></semantics></math></inline-formula> construction. It provides a birthday-bound security with 4 rounds and Beyond-Birthday-Bound (BBB for short) security with 10 rounds. Following their work, we further reduce the number of rounds in order to improve the efficiency while preserving the same level of security bound. More specifically, we rigorously prove that 6-round tweakable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">KAF</mi></semantics></math></inline-formula> cipher is BBB- secure. The main technical contribution is presenting a more refined security proof framework, which makes significant efforts to deal with several subtle and complicated sub-events. Note that Yan et al. showed that 4-round <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">KAF</mi></semantics></math></inline-formula> provides exactly Birthday-Bound security by a concrete attack. Thus, 6 rounds are (almost) minimal rounds to achieve BBB security for tweakable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">KAF</mi></semantics></math></inline-formula> construction.