Let G be a finite group and chi is an element of Irr(G). The codegree of chi is defined as cod(chi) = vertical bar G:ker(chi)vertical bar and cod(G) = {cod(chi) vertical bar chi is an element of Irr(G)} is called the set of codegrees of G. In this paper, we show that the set of codegrees of PSL(3, q) and PSU(3, q) determines the group up to isomorphism.