  The $\beta$-decay half-lives of $^{128\text{--}130}$Cd have been measured
with the newly commissioned GRIFFIN $\gamma$-ray spectrometer at the
TRIUMF-ISAC facility. The time structures of the most intense $\gamma$-rays
emitted following the $\beta$-decay were used to determine the half-lives of
$^{128}$Cd and $^{130}$Cd to be $T_{1/2}= 246.2(21)$ ms and $T_{1/2}= 126(4)$
ms, respectively. The half-lives of the 3/2$^+$ and 11/2$^-$ states of
$^{129}$Cd were measured to be $T_{1/2}(3/2^+)= 157(8)$ ms and
$T_{1/2}(11/2^-)= 147(3)$ ms. The half-lives of the Cd isotopes around the
$N=82$ shell closure are an important ingredient in astrophysical simulations
to derive the magnitude of the second $r$-process abundance peak in the
$A\sim130$ region. Our new results are compared with recent literature values
and theoretical calculations.
