  The quasinormal modes of a massless Dirac field in the de
Rham-Gabadadze-Tolley (dRGT) massive gravity theory with asymptotically de
Sitter spacetime are investigated using the Wentzel- Kramers-Brillouin (WKB)
approximation. The effective potential for the massless Dirac field due to the
dRGT black hole is derived. It is found that the shape of the potential depends
crucially on the structure of the graviton mass and the behavior of the
quasinormal modes is controlled by the graviton mass parameters. Higher
potentials give stronger damping of the quasinormal modes. We compare our
results to the Schwarzschild-de Sitter case. Our numerical calculations are
checked using Pad$\acute{e}$ approximation and found that the quasinormal mode
frequencies converge to ones with reasonable accuracy.
