We derived local boundary counterterms in massive gravity theory with a negative cosmological constant in four dimensions. With these counterterms at hand, we analyzed the properties of the boundary field theory in the context of AdS/CFT duality by calculating the boundary stress-energy tensor. The calculation shows that the boundary stress-energy tensor is conserved, and momentum dissipation might occur on the level of linear response only. We also calculated the thermodynamic quantities and the boundary stress-energy tensor for a specific type of solutions. The thermodynamic potentials agree with the results of literature up to some constants which can be removed by adding finite counterterms.