  We study the globular cluster system (GCS) of the giant elliptical NGC4374
(M84) in the Virgo cluster using B and R photometry. The colour distribution is
bimodal with peaks at B-R=1.11 and B-R=1.36, fitting well to those found in
other early-type galaxies. The radial profile of the cluster number density is
flatter than the galaxy light. Using the luminosity function we derive a
distance modulus of $\mu=31.61\pm0.2$, which within the uncertainty agrees with
the distance from surface brightness fluctuations. Blue and red clusters show
similar radial concentrations and azimuthal distributions. The total number of
clusters is $N=1775\pm150$, which together with our distance modulus leads to a
specific frequency of $S_{N}=1.6\pm0.3$. This value is surprisingly low for a
giant elliptical, but resembles the case of merger remnants like NGC1316, where
the low specific frequency is probably caused by the luminosity contribution of
an intermediate-age population. A further common property is the high rate of
type Ia supernovae which also may indicate the existence of a younger
population. However, unlike in the case of NGC1316, one cannot find any further
evidence that NGC4374 indeed hosts younger populations. The low specific
frequency would also fit to a S0 galaxy seen face-on.
