  The density dependent relativistic hadron field theory(DDRH) is extended to
inclusions of pentaquark $\Theta^+$. We investigate In-medium properties of
$\Theta^+$ and nucleons. As well as the neutron and proton,the effective
$\Theta^+$ mass decreases as the baryon density increases,and remains larger
than nucleons'. The effective mass of $\Theta^+$ is
calculated,$M^*_{\Theta^+}\simeq0.71M_{\Theta^+}$ at normal nuclear density
with the fraction of $\Theta^+$ 0.2. The effective masses of all baryon
increase with the increasing fraction of $\Theta^+$. The binding energy is also
studied. We find the binding energy is much larger than it in nuclear matter
without $\Theta^+$,and then discuss the stability of the system with
conclusions of pentaquark $\Theta^+$. It is shown that the system becomes
bounder added small fraction of $\Theta^+$. Finally we discuss the condition
when the system is the most stable and calculate the minimum of binding energy
and the fractions of all baryons as functions of baryon density.
