  We study the AdS rotating black hole solution for the
Bergshoeff-Hohm-Townsend (BHT) massive gravity in three dimensions. The field
equations of the asymptotically AdS black hole of the static metric can be
expressed as the first law of thermodynamics, i.e. $dE=TdS-PdV$. The corrected
Hawking-like temperature and entropy of asymptotically AdS rotating black hole
are calculated using the Cardy formula and the tunneling method. Comparison of
these methods will help identify the unknown leading correction parameter
$\beta_1$ in the tunneling method.
