IMPOSSIBLE DIFFERENTIAL attack is a well-known mean to examine robustness of block ciphers. Using IMPOSSIBLE DIFFERENTIAL cryptanalysis, we analyze security of a family of lightweight block ciphers, named Midori, that are designed considering low energy consumption. Midori state size can be either 64 bits for Midori64 or 128 bits for Midori128; however, both versions have key size equal to 128 bits. In this paper, we mainly study security of Midori64. To this end, we use various techniques such as early-abort, memory reallocation, miss-in-the-middle and turning to account the inadequate key schedule algorithm of Midori64. We first show two new 7-round IMPOSSIBLE DIFFERENTIAL characteristics which are, to the best of our knowledge, the longest IMPOSSIBLE DIFFERENTIAL characteristics found for Midori64. Based on the new characteristics, we mount three IMPOSSIBLE DIFFERENTIAL attacks on 10, 11, and 12 rounds on Midori64 with287: 7, 290: 63, and 290: 51 time complexity, respectively, to retrieve the master-key.