KASUMI is a block cipher which consists of eight Feistel rounds with a 128-bit key. Proposed more than 10 years ago, the confidentiality and integrity of 3G mobile communications systems depend on the security of KASUMI. In the practically interesting single key setting, only up to 6 rounds have been attacked so far. In this paper we use some observations on the FL and FO functions. Combining these observations with a key schedule weakness, we select some special input and output values to refine the general 5-round impossible differentials and propose the first 7-round attack on KASUMI with time and data complexities similar to the previously best 6-round attacks. This leaves now only a single round of security margin. The new impossible differential attack on the last 7 rounds needs 2114.3 encryptions with 252.5 chosen plaintexts. For the attack on the first 7 rounds, the data complexity is 262 known plaintexts and the time complexity is 2115.8 encryptions.