  In this paper, we test the dark matter-dark energy interacting cosmological
model with a dynamic equation of state $w_{DE}(z)=w_{0}+w_{1}z/(1+z)$, using
type Ia supernovae (SNe Ia), Hubble parameter data, baryonic acoustic
oscillation (BAO) measurements, and the cosmic microwave background (CMB)
observation. This interacting cosmological model has not been studied before.
The best-fitted parameters with $1 \sigma$ uncertainties are $\delta=-0.022 \pm
0.006$, $\Omega_{DM}^{0}=0.213 \pm 0.008$, $w_0 =-1.210 \pm 0.033$ and
$w_1=0.872 \pm 0.072$ with $\chi^2_{min}/dof = 0.990$. At the $1 \sigma$
confidence level, we find $\delta<0$, which means that the energy transfer
prefers from dark matter to dark energy. We also find that the SNe Ia are in
tension with the combination of CMB, BAO and Hubble parameter data. The
evolution of $\rho_{DM}/\rho_{DE}$ indicates that this interacting model is a
good approach to solve the coincidence problem, because the $\rho_{DE}$
decrease with scale factor $a$. The transition redshift is $z_{tr}=0.63 \pm
0.07$ in this model.
