For a graph G = (V, E), a double roman dominating function is a function f : V 0, 1, 2, 3 having the property that if f(v) = 0, then vertex vmust have at least two neighbors assigned 2under f or one neighbor with f(w) = 3, and if f(v) = 1, then vertex v must have at least one neighbor with f(w) 2. The weight of a double roman dominationg function f is the sum f(V ) = vV f(v), and the minimum weight of a double roman dominating functions on G is the double roman domination number of G. We initiate the study of double roman domination and show its relationship to both domination and Roman domination, Finally, we present an upper bound in terms of G and characterize the graphs attaining this bound