  The ellipsoidal BGK model is a generalized version of the original BGK model
designed to reproduce the physical Prandtl number in the Navier-Stokes limit.
In this paper, we propose a new implicit semi-Lagrangian scheme for the
ellipsoidal BGK model, which, by exploiting special structures of the
ellipsoidal Gaussian, can be transformed into a semi-explicit form,
guaranteeing the stability of the implicit methods and the efficiency of the
explicit methods at the same time. We then derive an error estimate of this
scheme in a weighted $L^{\infty}$ norm. Our convergence estimate holds
uniformly in the whole range of relaxation parameter $\nu$ including $\nu=0$,
which corresponds to the original BGK model.
