In organic chemistry, finding out theoretically the total π−electron energy of conjugated carbon compound is one of the interesting concept. Later during the year 1970, I. Gutman was successful in achieving this by defining a term called energy of a graph, E(G) for any graph G with m edges and n vertices. It is not that easy to find energy of any general graph. This problem was solved by obtaining bounds for E(G). Initially bounds for energy of any graph G are obtained by using McClelland bounds. Koolen and Moulton improved the McClelland’s upper bounds. In this article we established new energy bounds with the help of Holder’s inequality.