ESF is a lightweight block cipher based on a modified 32round Feistel structure. In order to study the ESF algorithm's ability to resist the impossible differential attack, we use relatedkey impossible differential cryptanalysis to analyze the security of ESF for the first time. And two 10round relatedkey impossible differential paths are constructed based on the characteristics of the key extended algorithm and the structure of round functions. Then a relatedkey impossible differential attack on 13round ESF is proposed by adding 1 round at the top and 2 rounds at the bottom to a 10round relatedkey impossible differential path. The attack has a complexity of 223 13round encryptions and about 260 chosen plaintexts with 18 recovered keybits. A relatedkey impossible differential attack on a 14round ESF is also proposed by adding 2 rounds both at the top and the bottom to another 10round relatedkey impossible differential path, which has a complexity of 243.95 14round encryptions and about 262 chosen plaintexts with 37 recovered keybits.