The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2 = y2. We call this graph an equal‐square graph of the finite group G, symbolized by ES(G). Some interesting properties of ES(G) are studied. Moreover, examples of equal‐square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units U(n), and the finite abelian groups are constructed.