  We investigate the asymptotic structure of the three dimensional warped anti
de sitter black holes in the Bergshoeff, Hohm and Townsend massive gravity
using the canonical Hamiltonian formalism. We define the canonical asymptotic
guage generators, which produce the conserved charges and the asymptotic
symmetry group for the warped anti de sitter black holes. The attained symmetry
group is described by a semi direct sum of a Virasoro and a KacMoody algebra.
Using the Sugawara construction, we obtain a direct sum of two Virasoro
algebras. We show that not only the asymptotic conserved charges satisfy the
first law of black hole thermodynamics, but also they lead to the expected
Smarr formula for the warped anti de sitter black holes. We also show that the
black hole entropy obeys the Cardy formula of the dual conformal field theory .
