  Motivated by the recently reported measurement of the $W$ boson mass $M_W =
80.4335 \pm 0.0094$ GeV by the CDF collaboration, we propose a type III seesaw
extension of the minimal supersymmetric standard model (MSSM) which also
includes an R-parity violating term. Without taking potential SUSY radiative
corrections into account, we show that the CDF measurement of $M_W$ and the LEP
measurement of the $\rho$ parameter can be simultaneously accommodated at the
$2 \sigma$ level. A long-lived gravitino in a few GeV mass range is a unique
viable dark matter candidate in this framework.
