We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reexiv e hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCIalgebras and hyper groups, and between hyper BCI-algebras and hyper Hv-groups.