The concept of maximum deficiency matrix Mdf (G) of a simple graph G is introduced in this paper. Let G = (V,E) be a simple graph of order n and let df(vi) be the deficiency of a vertex vi, i = 1, 2, . . . , n, then the maximum deficiency matrix Mdf (G) = [fij ]n×n is defined as: fij = ( max{df(vi), df(vj )}, if vivj 2 E(G) 0 , otherwise. Further, some coefficients of the characteristic polynomial (G; ) of the maximum deficiency matrix of G are obtained. The maximum deficiency energy EMdf (G) of a graph G is also introduced. The bounds for EMdf (G) are established. Moreover, maximum deficiency energy of some standard graphs is shown, and if the maximum deficiency energy of a graph is rational, then it must be an even integer.