  We study the orbital evolution of eccentric binary neutron stars. The orbit
is described as a Quasi-Keplarian orbit with perturbations due to tidal
couplings. We find that the tidal interaction between stars contributes to
orbital precession, in addition to the Post-Newtonian procession. The coupling
between the angular and radial motion of the binary also excites a series of
harmonics in the stars' oscillation. In the small eccentricity limit, this
coupling mainly gives rise to an additional orbital resonance, with the orbital
frequency being one third of the f-mode frequency. For a binary with initial
eccentricity $\sim 0.2$ at $50$Hz orbital frequency, the presence of this tidal
resonance introduces $\sim 0.5$ phase shift in the gravitational waveform till
merger, subject to uncertainties in neutron star equation of state and the
distribution of binary component masses. Such phase shift in the late-inspiral
stage is likely detectable with third-generation gravitational-wave detectors.
