Artificial structures with negative permittivity or permeability have attracted significant attention in the science community because they provide a pathway for obtaining exotic electromagnetic properties not found in natural materials. At the moment, the great challenge of these artificial structures in microwave frequency exhibits a relatively large loss. It is well-known that superconducting thin films have extremely low surface resistance. Hence, it is a good candidate to resolve this constraint. Besides, the reported artificial structures with negative permittivity or permeability are mainly focusing on linear regime of wave propagation. However, any future effort in creating tunable structures would require knowledge of nonlinear properties. In this work, a tunable superconducting filter with composite right/left-hand transmission property is proposed and fabricated. Its nonlinear effects on temperature and power are studied by theoretical analysis and experiments.