  We forecast the constraints on cosmological parameters in the interacting
dark energy model using the mock data generated for neutral hydrogen intensity
mapping (IM) experiments. In this work, we consider only the interacting dark
energy model with the energy transfer rate $Q=\beta H\rho_{\rm c}$, and take
BINGO, FAST, SKA1-MID, and Tianlai as typical examples of the 21 cm IM
experiments. We find that the Tianlai cylinder array will play an important
role in constraining the interacting dark energy model. Assuming perfect
foreground removal and calibration, and using the Tianlai-alone data, we obtain
$\sigma(H_0)=0.10$ km s$^{-1}$ Mpc$^{-1}$, $\sigma(\Omega_{\rm m})=0.0013$, and
$\sigma(\sigma_8)=0.0015$ in the I$\Lambda$CDM model, which are much better
than the results of Planck+optical BAO (i.e. optical galaxy surveys). However,
the Tianlai-alone data cannot provide very tight constraint on the coupling
parameter $\beta$, compared with Planck+optical BAO, while the Planck+Tianlai
data can give a rather tight constraint of $\sigma(\beta)=0.00052$, due to the
parameter degeneracies being well broken by the data combination. In the
I$w$CDM model, we obtain $\sigma(\beta)=0.00058$ and $\sigma(w)=0.006$ from
Planck+Tianlai. In addition, we also make a detailed comparison among BINGO,
FAST, SKA1-MID, and Tianlai in constraining the interacting dark energy model.
We show that the future 21 cm IM experiments will provide a useful tool for
exploring the nature of dark energy, and will play a significant role in
measuring the coupling between dark energy and dark matter.
