We introduce a structure made of periodic arrays of H-shaped metallic pattern that offers a potentially simple approach in building left-handed metamaterials with simultaneous negative permittivity and permeability. We have investigated experimentally the transmittance in the rectangle waveguide and found unambiguously a passband that can be tuned easily at microwave frequencies by changing the parameter t. Using phase shift experiment, prism refraction experiment and S-parameter retrieval method, we have confirmed that the H-shaped metamaterials have negative refractive indices, negative permittivity and negative permeability at the passband frequencies. Compared with the conventional left-handed metamaterials consisting of arrays of wires and split ring resonators, H-shaped left-handed metamaterials show not only magnetic resonance but also electric resonance, so they will be a good candidate in the microwave applications due to their simple structure and easy preparation.