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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-bosonexchange model with light meson exchanges plus a short-range $J/\psi$ exchange.The scattering amplitude is calculated within a Bethe-Salpeter equationapproach and the poles near the $D\bar{D}^*$ threshold are searched. In theisoscalar sector, two poles found under the $D\bar{D}^*$ threshold, i.e., boundstates, 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 boundstate with $I^G(J^P)=1^+(1^+)$ is found with a large cutoff at about 3 GeV. Ifa cutoff at about 2 GeV is adopted with which a pole carrying the quantumnumber of the $X(3872)$ is produced at an energy of about 3871 MeV, the polefor the bound state with $1^+(1^+)$ runs across the threshold to a secondRienman sheet and becomes a resonance above the $D\bar{D}^*$ threshold, whichcan 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 foundby BESIII can be reproduced.

$Z_c(3900)$ as a resonance from the $D\bar{D}^*$ interaction