Left-handed material (LHM), whose permittivity and permeability are both negative, has attracted much attention due to its exotic electromagnetic properties, such as negative refraction, backward wave propagation and evanescent wave amplification. The microwave left-handed property of a composite medium composed of ferrite cubes’ array and copper net was studied using the method of finite difference time domain in this paper. An obvious left-handed pass band emerged when ferrite cubes were combined with longitudinal copper wires, because the ferrite produced negative permeability by the ferromagnetic resonance and the copper wires produced negative permittivity by the plasma. With the addition of horizontal copper wires, the transmission intensity of the pass band was gradually weakened. It can be concluded that the horizontal wires played a negative role in realizing the composite LHM with ferrite cubes and copper net. This work gives an instructive direction to the fabrication of 3D LHMs.