Summary: Constructions of quantum distinguishers (extended to key recovery attacks) for generalized Feistel networks have been recently proposed in several works, where the main focus has been on Type 1 and 2 schemes. In this work, we derive a quantum distinguisher for 7 and 8 rounds of the SMS4 block cipher, which belongs to the class of unbalanced (contracting) generalized Feistel schemes. In the former case, by applying Simon’s quantum algorithm we construct a quantum distinguisher that runs in (quantum) polynomial time \(\mathcal{O}(n)\) (\(n\) is the branch size), while later we need to combine Simon’s and Grover’s algorithms in context of the amplitude amplification technique. We show that for the 8-round SMS4 cipher a quantum distinguisher can be constructed in both \(\mathbf{Q1}\) and \(\mathbf{Q2}\) attack models. This is achieved by applying the method of asymmetric search of a period, introduced by X. Bonnetain and M. Naya-Plasencia [Lect. Notes Comput. Sci. 11272, 560–592 (2018; Zbl 1446.94106)], where online and offline queries to the encryption oracle are separated. In this context, we answer the open problem posed by X. Dong, Z. Li and X. Wang [“Quantum cryptanalysis on some generalized Feistel schemes”, Sci. China Inf. Sci. 62, Paper No. 22501, 12 p. (2019; doi:10.1007/s11432-017-9436-7)], which has been left open for construction of quantum distinguishers for \(\geq 7\) rounds. Moreover, we show that for the specific instance when the quantum oracle for 8 rounds of SMS4 cipher is available, one can extract the master secret key with the same complexity and number of qubits required for the 8-round distinguisher.