Let G be a graph with n vertices and m edges. The term energy of a graph G was introduced by I. Gutman in chemistry due to its relevance to the total p-electron energy of a carbon compound. An analogous energy E D( G), called the distance energy, was defined by Indulal et al. ( MATCH Commun. Math. Comput. Chem. 60: 461-472, 2008) in 2008. McClelland and Koolen-Moulton bounds for distance energy were established subsequently by Ramane et al. ( Kragujev. J. Math. 31: 59-68, 2008). The lower and upper bounds for E D( G) obtained in this paper are better than the McClelland and Koolen-Moulton bounds.