  We systematically investigated the low-temperature transport properties of a
series of NbN epitaxial films with thickness $t$ ranging from $\sim$2.0 to
$\sim$4.0 nm. The films undergo a superconductor-insulator transition (SIT)
with decreasing film thickness, and the critical sheet resistance for the SIT
is close to the quantum resistance of Cooper pairs $h/4e^2$ (6.45 k$\Omega$).
Besides the Berezinski-Koterlitz-Thouless transition, a magnetic-field-driven
SIT is observed in those two-dimensional (2D) superconducting films (2.6 nm
$\lesssim t \lesssim 4.0$ nm). Interestingly, it is found that the
low-temperature magnetoresistance isotherms do not cross at a single fixed
point but at a well-distinguished region for these superconducting films. The
dynamical critical exponent obtained by analyzing these magnetoresistance
isotherms is divergent as the quantum critical point is being approached. The
behavior of the dynamical critical exponent, originating from quenched disorder
at ultralow temperatures, provides direct evidence for the occurrence of
quantum Griffiths singularity in the quantum phase transition process of the
films. The field-driven anomalous metal (quantum metal) state does not appear
in these films. Our results suggest that the quantum Griffiths singularity not
only occurs in the highly crystalline 2D superconductors with
superconductor-metal transition but also in those with SIT.
