Let \(R\) be a ring with 1, \(C\) the center of \(R\), \(R[x]\) the polynomial ring with an indeterminate \(x\), and \(R[x,x^{-1}]\) the Laurent polynomial ring. If \((\sum_{i=0}^n a_ix^i)(\sum_{j=0}^m b_jx^j)=0\) for \(\sum_{i=0}^n a_ix^i,\sum_{j=0}^m b_jx^j\not=0\) in \(R[x]\) implies that \(a_ib_j\in C\) for all \(i\) and \(j\), then \(R\) is called a central Armendariz ring. An Armendariz ring is a central Armendariz ring, but the converse is false. Theorem. The following are equivalent: (1) A ring \(R\) is a central Armendariz ring, (2) \(R[x]\) is a central Armendariz ring, (3) \(R[x,x^{-1}]\) is a central Armendariz ring, (4) \(S^{-1}R\) is a central Armendariz ring where \(S^{-1}R\) is the localization of \(R\) at the set \(S\) of central regular elements in \(R\). -- Moreover, relations of a central Armendariz ring to other classes of rings are also given such as matrix rings, reduced rings, and Abelian rings.