For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${frac}{G}{Z(G)$${cong}D_8$,$A_4$, $Z_2{ imes}Z_2{ imes}Z_2$ or $Z_2{ imes}Z_2{ imes}Z_2{ imes}Z_2$.