In this paper, we experimentally realize a one-dimensional RHM (Right-handed Material)-LHM (Left-handed Material) multi-frequency resonator that consists of a dual-negative-band LHM and air arranged in an X-band waveguide. Multi-resonant frequencies are observed within two left-handed bands of the LHM. The effects of the loss and the hyperbolic dispersion relation of LHM layer are discussed. The incorporation of such a LHM into the resonator design allows more flexibility to realize multi-resonance.