As one of the ten block cipher algorithms selected for the second round of the 2018 National Cryptographic Algorithm Design Contest, Feistel-based block cipher (FBC) is an efficient and lightweight block cipher algorithm with a four-branch and two-fold Feistel structure. In this study, the FBC algorithm is abstracted as the FBC model, and the pseudorandomness and super-pseudorandomness of the model are studied. It is assumed that the FBC round functions are independent random functions, and a method to find the minimal number of FBC rounds is provided, which will keep FBC indistinguishable from a random permutation. Finally, the study comes to the conclusion that under the chosen-plaintext attack, four rounds of FBC are indistinguishable from random permutation, so the model has pseudorandomness; under the adaptive chosen-plaintext and ciphertext attack, five rounds of FBC are indistinguishable from random permutation, so the model has super-pseudorandomness.