With the advancement of quantum computing, the security of cryptographic structures is facing significant challenges. In this paper, we present new quantum attacks on the Generalized Feistel Structures proposed by Wu and Wang. For New Structure IV, the best-known distinguisher is the 9-round distinguisher proposed by Li and Liu at INSCRYPT 2024. Based on this 9-round distinguisher, Li and Liu achieved a r-round ( \(r > 9\) ) key-recovery attack with a time complexity of \(O(2^{(r-9)k/2})\) . In this work, we identify a new property that enables the extension of the periodic distinguisher for this structure by 6 rounds. Specifically, we construct a 6-round periodic distinguisher that satisfies this property, which allows us to obtain a 12-round distinguisher, improving the previous best result by 3 rounds. Finally, by applying the Grover-meet-Simon algorithm, we achieve a quantum key-recovery attack on the r-round ( \(r > 12\) ) New Structure IV with a time complexity of \(O(2^{(r-12)k/2})\) , which represents the best key-recovery attack for this structure.