  Time reversal and spatial inversion are two key symmetries for conventional
Bardeen-Cooper-Schrieffer (BCS) superconductivity. Breaking inversion symmetry
can lead to mixed-parity Cooper pairing and unconventional superconducting
properties. Two-dimensional (2D) NbSe$_2$ has emerged as a new
non-centrosymmetric superconductor with the unique out-of-plane or Ising
spin-orbit coupling (SOC). Here, we report the observation of an unusual
continuous paramagnetic-limited superconductor-normal metal transition in 2D
NbSe$_2$. Using tunneling spectroscopy under high in-plane magnetic fields, we
observe a continuous closing of the superconducting gap at the upper critical
field at low temperatures, in stark contrast to the abrupt first-order
transition observed in BCS thin film superconductors. The paramagnetic-limited
continuous transition arises from a large spin susceptibility of the
superconducting phase due to the Ising SOC. The result is further supported by
self-consistent mean-field calculations based on the ab initio band structure
of 2D NbSe$_2$. Our findings establish 2D NbSe$_2$ as a promising platform for
exploring novel spin-dependent superconducting phenomena and device concepts,
such as equal-spin Andreev reflection and topological superconductivity.
