  In this paper it is proposed that the charged charmonium-like state
$Z_c(3900)$ is a resonance above the threshold from the $D\bar{D}^*$
interaction. The $D\bar{D}^*$ interaction is described by the one-boson
exchange model with light meson exchanges plus a short-range $J/\psi$ exchange.
The scattering amplitude is calculated within a Bethe-Salpeter equation
approach and the poles near the $D\bar{D}^*$ threshold are searched. In the
isoscalar sector, two poles found under the $D\bar{D}^*$ threshold, i.e., bound
states, have the quantum numbers $I^G(J^{PC})=0^-(1^{+-})$ and $0^+(1^{++})$.
The latter can be related to the $X(3872)$. In the isovector sector, a bound
state with $I^G(J^P)=1^+(1^+)$ is found with a large cutoff at about 3 GeV. If
a cutoff at about 2 GeV is adopted with which a pole carrying the quantum
number of the $X(3872)$ is produced at an energy of about 3871 MeV, the pole
for the bound state with $1^+(1^+)$ runs across the threshold to a second
Rienman sheet and becomes a resonance above the $D\bar{D}^*$ threshold, which
can be identified with the $Z_c(3900)$. With such a cutoff, the $D\bar{D}^{*}$
invariant mass spectrum is also investigated and the experimental results found
by BESIII can be reproduced.
