  Solar filament are commonly thought to be supported in magnetic dips, in
particular, of magnetic flux ropes (FRs). In this Letter, from the observed
photospheric vector magnetogram, we implement a nonlinear force-free field
(NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale
intermediate filament between an active region and a weak polarity region. This
result is the first in that current NLFFF extrapolations with presence of FRs
are limited to relatively small-scale filaments that are close to sunspots and
along main polarity inversion line (PIL) with strong transverse field and
magnetic shear, and the existence of a FR is usually predictable. In contrast,
the present filament lies along the weak-field region (photospheric field
strength $\lesssim 100$ G), where the PIL is very fragmented due to small
parasitic polarities on both side of the PIL and the transverse field has a low
value of signal-to-noise ratio. Thus it represents a far more difficult
challenge to extrapolate a large-scale FR in such case. We demonstrate that our
CESE--MHD--NLFFF code is competent for the challenge. The numerically
reproduced magnetic dips of the extrapolated FR match observations of the
filament and its barbs very well, which supports strongly the FR-dip model for
filaments. The filament is stably sustained because the FR is weakly twisted
and strongly confined by the overlying closed arcades.
