  We consider a minimizing movement scheme of Chambolle type for the mean
curvature flow equation with prescribed contact angle condition in a smooth
bounded domain in $\mathbb{R}^d$ ($d\geq2$). We prove that an approximate
solution constructed by the proposed scheme converges to the level-set mean
curvature flow with prescribed contact angle provided that the domain is convex
and that the contact angle is away from zero under some control of derivatives
of given prescribed angle. We actually prove that an auxiliary function
corresponding to the scheme uniformly converges to a unique viscosity solution
to the level-set equation with an oblique {derivative} boundary condition
corresponding to the prescribed boundary condition.
