  Here we report the discovery of pressure-induced superconductivity in
quasi-one-dimensional $\mathrm{Ta}_2 \mathrm{PdSe}_6$, through a combination of
electrical transport, synchrotron x-ray diffraction, and theoretical
calculations. Our transport measurements show that the superconductivity
appears at a critical pressure $P_{\mathrm{c}} \sim 18.3$ GPa and is robust
upon further compression up to $62.6$ GPa. The estimated upper critical field
$\mu_0 H_{\mathrm{c} 2}(0)$ in the pressurized $\mathrm{Ta}_2 \mathrm{PdSe}_6$
is much lower than the Pauli limiting field, in contrast to the case in its
isostructural analogs $M_2 \mathrm{Pd}_{\mathrm{x}} X_5$ $(M=\mathrm{Nb}$, Ta;
$X=\mathrm{S}, \mathrm{Se})$. Concomitant with the occurrence of
superconductivity, anomalies in pressuredependent transport properties are
observed, including sign reversal of Hall coefficient, abnormally enhanced
resistance, and dramatically suppressed magnetoresistance. Meanwhile,
room-temperature synchrotron x-ray diffraction experiments reveal the stability
of the pristine monoclinic structure (space group $C 2 / m$ ) upon compression.
Combined with the density functional theory calculations, we argue that a
pressure-induced Lifshitz transition could be the electronic origin of the
emergent superconductivity in $\mathrm{Ta}_2 \mathrm{PdSe}_6$.
