Eccentricity based topological indices have attracted large attraction in the field of chemical graph theory. Eccentricity based topological indices are prominent due to their wide range applications. With the help of eccentricity based topological indices we can predict excellent accuracy rate in certain biological activities of diverse nature as com-pared to other indices. Carbon nanotubes are the cylindrical molecules that consist of rolled up sheets of carbon atoms. In this paper we consider the chemical graph of NA(m)(n) nanotube and compute an important eccentricity based topological index called Modified eccentric connectivity index.