  We study the vortex dynamics in high-quality FeTe$_{0.6}$Se$_{0.4}$ single
crystal by performing magnetization measurements of the screening current
density \emph{J}$_s$ and flux creep rate \emph{S}. Temperature dependence of
\emph{S} shows a plateau in the intermediate temperature region with a high
creep rate $\sim$ 0.03, which is interpreted in the framework of the collective
creep theory. A crossover from elastic to plastic creep is observed. The glassy
exponent and barrier height for flux creep are directly determined by extended
Maley's method. \emph{J}$_s$ with flux creep, obtained from magnetic hysteresis
loops, is successfully reproduced based on the collective creep analysis. We
also approach critical current density without flux creep by means of the
generalized inversion scheme, which proves that the $\delta$\emph{l} and
$\delta$\emph{T}$_c$ pinning coexist in FeTe$_{0.6}$Se$_{0.4}$ single crystal.
