  Recently, a practical approach to holographic renormalization has been
developed based on the Hamilton-Jacobi formulation. Using a simple
Einstein-scalar theory, we clarify that this approach does not conflict with
the Hamiltonian constraint as it seems. Then we apply it to the holographic
renormalization of massive gravity. We assume that the shift vector is falling
off fast enough asymptotically. We derive the counterterms up to the boundary
dimension d=4. Interestingly, we find that the conformal anomaly can even occur
in odd dimensions, which is different from the Einstein gravity. We check that
the counterterms cancel the divergent part of the on-shell action at the
background level. At the perturbation level, they are also applicable in
several time-dependent cases.
