The study of lightweight block ciphers has been a “hot topic”. As one of the main structures of block ciphers, the Feistel structure has attracted much attention. However, the traditional Feistel structure cipher changes only half of the plaintext in an iterative round, resulting in slow diffusion. Therefore, more encryption rounds are required to ensure security. To address this issue, a new algorithm, GFRX, is proposed, which combines a generalized Feistel structure and ARX (Addition or AND, Rotation, XOR). The GFRX algorithm uses an ARX structure with different non-linear components to deal with all the branches of a generalized Feistel structure so that it can achieve a better diffusion effect in fewer rounds. The results of a security analysis of the GFRX algorithm show that the effective differential attacks do not exceed 19 rounds and that the effective linear attacks do not exceed 13 rounds. Therefore, the GFRX algorithm has an adequate security level for differential and linear analysis. Avalanche test results obtained for the GFRX algorithm show that the GFRX algorithm has strong diffusion and only takes six rounds to meet the avalanche effect. In addition, the GFRX algorithm can achieve different serialization levels depending on different hardware resource requirements and can achieve full serialization, which ensures operational flexibility in resource-constrained environments.