Abstract: n-FI injective modules were generalized to the complex level. Firstly, we gave the definition of  n-FI injective complexes. Secondly, we proved that a complex C was n-FI injective complex if and only if each term was n-FI injective module  and Hom(X,C) was acyclic for any complex X with FP-id(X)≤n. Finally, n-FI injective complexes were characterized by covers of complexes.

Key words: n-FI injective module, FP-injective complex, n-FI injective complex