SAFER block cipher family consists of SAFER K, SAFER SK, SAFER+ and SAFER++. As the first proposed block cipher of them, SAFER K is strengthened by SAFER SK with improved key schedule. SAFER+ is designed as an AES candidate and Bluetooth uses a customized version of it for security. SAFER++, a variant of SAFER+, is among the cryptographic primitives selected for the second phase of the NESSIE project. In this paper, we take advantage of properties of the linear transformation and S-boxes to identify new impossible differentials for SAFER SK, SAFER+, and SAFER++. Moreover, we give the impossible differential attacks on 4-round SAFER SK/128 and 4-round SAFER+/128(256), 5-round SAFER++/128 and 5.5-round SAFER++/256. Our attacks significantly improve previously known impossible differential attacks on them. Specifically, our attacks on SAFER+ are the best attack in terms of number of rounds.