  We report superconductivity in Sn$_{x}$NbSe$_{2-\delta}$, a topological
nodal-line semimetal candidate with a noncentrosymmetric crystal structure. The
superconducting transition temperature $T_{c}$ of this compound is extremely
sensitive to Sn concentration $x$ and Se deficiency $\delta$, 5.0 K for
Sn$_{0.13}$NbSe$_{1.70}$ and 8.6 K for Sn$_{0.14}$NbSe$_{1.71}$ and
Sn$_{0.15}$NbSe$_{1.69}$. In all samples, the temperature dependence of the
upper critical field $H_{c2}(T)$ differs from the prediction of the
Werthamer-Helfand-Hohenberg theory. While the zero-temperature value of the
in-plane upper critical field of Sn$_{x}$NbSe$_{2-\delta}$ with the higher
$T_{c}$ is lower than the Pauli paramagnetic limit $H_{P}$, that of the lower
$T_{c}$ sample exceeds $H_{P}$ by a factor of $\sim$2. Our observations suggest
that odd-parity contribution dominates the superconducting gap function of
Sn$_{x}$NbSe$_{2-\delta}$, and it can be fine-tuned by the Sn concentration and
Se deficiency.
