This study investigates meet-in-the-middle attacks on three types of unbalanced generalized Feistel structures and conducts quantum meet-in-the-middle attacks in Q1 model. First, for the 3-branch Type-III generalized Feistel structure, a 4-round meet-in-the-middle distinguisher is constructed using multiset and differential enumeration techniques. By expanding one round forward and one round backward, a 6-round meet-in-the-middle attack is conducted. With the help of Grover’s algorithm and the quantum claw finding algorithm, a 6-round quantum key recovery attack is performed, requiring O(2^3l/2·l) quantum queries, where l is the branch length of the generalized Feistel structure. Then, for the 3-branch Type-I structure, a 9-round distinguisher is similarly extended by one round in both directions to conduct an 11-round meet-in-the-middle attack and a quantum key recovery attack with time complexities of O(2^2l) 11-round encryptions and O(2^3l/2·l) quantum queries. Finally, taking the 3-cell generalized Feistel structure as a representative case, this study explores a quantum meet-in-the-middle attack on an n-cell structure. A 2n-round meet-in-the-middle distinguisher is constructed, enabling a 2(n+1)-round meet-in-the-middle attack and quantum key recovery attack. The associated time complexities are O(2^2l) 2(n+1)-round encryptions and O(2^3l/2·l) quantum queries. The results demonstrate that the time complexity in Q1 model is significantly reduced compared with classical scenarios.