  We investigate the influence of disorders in terminal ethylene groups of
BEDT-TTF molecules (ethylene-disorders) on the vortex pinning of the organic
superconductor $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br. Magnetization
measurements are performed under different cooling-processes. The second peak
in the magnetization hysteresis curve is observed for all samples studied, and
the hysteresis width of the magnetization becomes narrower by cooling faster.
In contradiction to the simple pinning effect of disorder, this result shows
the suppression of the vortex pinning force by introducing more
ethylene-disorders. The ethylene-disorder domain model is proposed for
explaining the observed result. In the case of the system containing a moderate
number of the ethylene-disorders, the disordered molecules form a domain
structure and it works as an effective pinning site. On the contrary, an excess
number of the ethylene-disorders may weaken the effect of the domain structure,
which results in the less effective pinning force on the vortices.
