  The detection of GRB 060218 at z=0.033 by {\em Swift} within 1.5 years of
operation, together with the detection of GRB 980425 at $z=0.0085$ by BeppoSAX,
suggest that these low-luminosity (LL) GRBs have a much higher event rate than
the canonical high-luminosity (HL) GRBs, and they form a distinct new component
in the GRB luminosity function. We explore the contribution of this previously
neglected GRB population to the diffuse neutrino background within the internal
shock model and compare it with that of the canonical HL population. By
considering a wide range of distributions of various parameters (e.g.
luminosity, spectral break energy, duration, variability time, Lorentz factor,
redshift) for both populations, we find that although it is difficult to detect
neutrinos from the individual LL GRBs, the contribution of the LL population to
the diffuse neutrino background is more than the HL population above about
$10^{8}$ GeV.
