A Ducci sequence generated by A = (a1, a2, ..., an) ∈ Zn is the sequence {A, DA, D2A, ...} where the Ducci map D : Zn → Zn is defined by D(A) = D(a1, a2, ..., an) = (|a2 − a1| ,|a3 − a2|, ..., |an − an−1|, |an − a1|). In this study, we examine some properties of the matrices Cn, DCn, D2Cn, where Cn =Circ(c0, c1, ..., cn−1) is a circulant matrix whose entries consist of Fibonacci numbers.