In 1999, Dontchev studied the concept of pre-I-open sets (Dontchev, 1999). In 2002, Hatir and Noiri studied the concept of semi-I-open sets (Hatir and Noiri, 2002). In 2013, Ekici studied the concept of C-I*-sets (Ekici, 2013). In this paper, the concept of zeta-I-open sets is introduced. The concept of zeta-I-open sets is related to topology, pre-I-open sets, semi-I-open sets and C-I*-sets. Main properties of zeta-I-open sets are presented. (C) 2017 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.