  We report the synthesis and physical properties of a full Heusler compound,
MgPd$_2$Sb, which we found to show superconductivity below $T_c$ = 2.2 K.
MgPd$_2$Sb was obtained by a two-step solid-state reaction method and its
purity and cubic crystal structure (Fm-3m, a=6.4523(1) \r{A}) were confirmed by
powder x-ray diffraction. Normal and superconducting states were studied by
electrical resistivity, magnetic susceptibility, and heat capacity
measurements. The results show that MgPd$_2$Sb is a type-II, weak coupling
superconductor ($\lambda_{e-p}$ = 0.53). The observed pressure dependence of
$T_c$ ($\Delta T_c / p \approx $ -0.23 K/GPa) is one of the strongest reported
for a superconducting Heusler compound. The electronic structure, phonons, and
electron-phonon coupling in MgPd$_2$Sb were theoretically investigated. The
obtained results are in agreement with the experiment, confirming the
electron-phonon coupling mechanism of superconductivity. We compare the
superconducting parameters tothose of all reported Heusler-type
superconductors.
