  We report the synthesis and superconducting properties of a new
transition-metal chalcogenide Ta$_2$PdSe$_5$. The measurements of resistivity,
magnetization, and specific heat reveal that Ta$_2$PdSe$_5$ is a bulk
superconductor with $T_c$ $\simeq$ 2.5 K. The zero-field electronic specific
heat in the superconducting state can be fitted with a two-gap BCS model. The
upper critical field $H_{c2}$ shows a linear temperature dependence, and the
value of $H_{c2}$(0) is much higher than the estimated Pauli limiting field
$H_{c2}^{P}$ and orbital limiting field $H_{c2}^{orb}$. All these results of
specific heat and upper critical field suggest that Ta$_2$PdSe$_5$ is a
multi-band superconductor.
