  We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT)
massive gravity with a cosmological constant. In the space of coupling
constants $(\Lambda_0,m^2)$, our canonical analysis reveals the special role of
the condition $\Lambda_0/m^2\neq-1$. In this sector, the dimension of the
physical phase space is found to be $N^*=4$, which corresponds to two
Lagrangian degree of freedom. When applied to the AdS asymptotic region, the
canonical approach yields the conserved charges of the BTZ black hole, and
central charges of the asymptotic symmetry algebra.
