  We explore a scenario of interacting dynamical dark energy model with the
interaction term $Q$ including the varying equation-of-state parameter $w$.
Using the data combination of the cosmic microwave background, the baryon
acoustic oscillation, and the type Ia supernovae, to global fit the interacting
dynamical dark energy model, we find that adding a factor of the varying $w$ in
the function of $Q$ can change correlations between the coupling constant
$\beta$ and other parameters, and then has a huge impact on the fitting result
of $\beta$. In this model, the fitting value of $H_{0}$ is lower at the $3.54
\sigma$ level than the direct measurement value of $H_{0}$ . Comparing to the
case of interacting dynamical dark energy model with $Q$ excluding $w$, the
model with $Q$ including the constant $w$ is more favored by the current
mainstream observation. To obtain higher fitting values of $H_{0}$ and narrow
the discrepancy of $H_{0}$ between different observations, additional
parameters including the effective number of relativistic species, the total
neutrino mass, and massive sterile neutrinos are considered in the interacting
dynamical dark energy cosmology. We find that the $H_{0}$ tension can be
further reduced in these models, but is still at the about $3 \sigma$ level.
