  Let $\mathcal{A}$ be a factor von Neumann algebra and $\phi$ be the
$\ast$-Jordan derivation on $A$, that is, for every $A,B \in \mathcal{A}$,
  $\phi(A\diamond_{1} B) = \phi(A)\diamond_{1} B + A\diamond_{1}\phi( B)$ where
$A\diamond_{1} B = AB + BA^{\ast}$, then $\phi$ is additive $\ast$-derivation.
