  After the experimental observation of charged and neutral $Z_c(3900)$, it is
of prime importance to pursue searches for additional production modes of these
exotic states. In this work, we investigate the possibility to study the
$Z_c(3900)$ through weak decays of b-baryons at the LHCb. Decay amplitudes for
various processes have been parametrized in terms of the SU(3) irreducible
nonperturbative amplitudes. A number of relations for the partial decay widths
are deduced from these results. The decay widths of $\Lambda_b^0\to \Lambda^0
Z_c^0(3900)$, $\Xi_b^- \to \Sigma^- Z_{c}^0(3900)$ and $\Xi_b^0 \to \Lambda^0
Z_{c}^0(3900)$ have also been calculated from which some relevant partial decay
widths of b-baryons could be estimated. The results presented in this paper can
be tested experimentally at hadron colliders in the future.
