Studies on the norms of the elementary operators on JB* -algebras Prime C * -algebras, Calkin algebras and standard operator algebras has been considered. In this paper, we characterize norm inequalities for Jordan elementary operators on C * -algebras. The results show that if H is an infinite dimensional complex Hilbert space and B(H) the C*-algebra of all bounded linear operators on H, then for a Jordan elementary operator U : B(H) → B(H) defined by: U(T) = PTQ + QTP for all T ϵ B(H) and Pi;Qi fixed in B(H), ║U(T)║ ≤ 2║P║║Q║. Moreover, if Pi and Qi are diagonal operators induced by {  ni} and {βni}respectively and H an infinite dimensional complex Hilbert space then U is bounded and║U║ = (Σn{Σ l i=1|  ni | 2 | βni | 2 }) 1/2 .