  We report the achieving of depairing current limit along $c$-axis in
Fe$_{1+y}$Te$_{1-x}$Se$_x$ single crystals. A series of crystals with
$T_{\rm{c}}$ ranging from 8.6 K to 13.7 K (different amount of excess Fe, $y$)
were fabricated into $c$-axis bridges with a square-micrometer cross-section.
The critical current density, $J_{\rm{c}}$, was directly estimated from the
transport current-voltage measurements. The transport $J_{\rm{c}}$ reaches a
very large value, which is about one order of magnitude larger than the
depinning $J_{\rm{c}}$, but comparable to the calculated depairing $J_{\rm{c}}$
$\sim$ 2 $\times$ 10$^6$ A/cm$^2$ at 0 K, based on the Ginzburg-Landau (GL)
theory. The temperature dependence of the depairing $J_{\rm{c}}$ follows the
GL-theory ($\propto$ (1-$T/T_{\rm{c}}$)$^{3/2}$) down to $\sim$ 0.83
$T_{\rm{c}}$, then increases with a reduced slope at low temperatures, which
can be qualitatively described by the Kupriyanov-Lukichev theory. Our study
provides a new route to understand the behavior of depairing $J_{\rm{c}}$ in
iron-based superconductors in a wide temperature range.
