  We study the microcausality of free Dirac field on noncommutative spacetime.
We calculate the vacuum and non-vacuum state expectation values for the Moyal
commutator $[\bar{\psi}_{\alpha}(x)\star\psi_{\beta}(x),\bar{\psi}_
{\sigma}(x^{\prime})\star\psi_{\tau}(x^{\prime})]_{\star}$ of Dirac field on
noncommutative spacetime. We find that they do not vanish for some cases of the
indexes for an arbitrary spacelike interval, no matter whether $\theta^{0i}=0$
or $\theta^{0i}\neq0$. However for the physical observable quantities of Dirac
field such as the Lorentz scalar $:\bar{\psi}(x)\star\psi(x):$ and the current
$j^{\mu}(x)=:\bar{\psi}(x)\gamma^{\mu}\star\psi(x):$ etc., we find that they
still satisfy the microcausality. Therefore microcausality is satisfied for
Dirac field on noncommutative spacetime.
