  We performed millimeter observations in CO lines toward the supernova remnant
(SNR) G127.1+0.5. We found a molecular filament at 4--13 km s$^{-1}$ consisting
of two distinct parts: a straight part coming out of the remnant region and a
curved part in the remnant region. The curved part is coincides well with the
bright SNR shell detected in 1420 MHz radio continuum and mid-infrared
observations in the northeastern region. In addition, redshifted line wing
broadening is found only in the curved part of the molecular filament, which
indicates a physical interaction. These provide strong evidences, for the first
time, to confirm the association between an SNR and a pre-existing long
molecular filament. Multi-band observations in the northeastern remnant shell
could be explained by the interaction between the remnant shock and the dense
molecular filament. RADEX radiative transfer modeling of the quiet and shocked
components yield physical conditions consistent with the passage of a
non-dissociative J-type shock. We argue that the curved part of the filament is
fully engulfed by the remnant's forward shock. A spatial correlation between
aggregated young stellar objects (YSOs) and the adjacent molecular filament
close to the SNR is also found, which could be related to the progenitor's
activity.
