PUFFIN is a block cipher with 64-bit block size and 128-bit key size. For evaluating its security, the balance at bit-level was analyzed. A 5-round integral distinguisher was constructed and then extended to a 6-round one based on the theory of higher order integral. By using the 6-round distinguisher, 8-round attack was performed. For 8-round attack, the data complexity, time complexity and space complexity were, and respectively. The result shows that PUFFIN reduced to 8 rounds is not immune to the integral attack. Besides, the cipher with SPN-structure and permutation-linear layer which at least has 3-round integral distinguisher is proved. The result also indicates the method for finding the distinguisher.