The generation of a second-harmonic wave, which is one typical nonlinear feature, is enhanced in a composite of plasma and metamaterial. When we generate plasma by an injection of microwaves, whose frequencies are fundamental, we observe intensified second-harmonic waves in the cases of negative-refractive-index states in which both metamaterial permeability and plasma permittivity are negative for the fundamental waves. We performed the measurements at multiple levels of microwave input power up to 300 W to regulate permittivity in the negative polarity for the fundamental wave and in the transient region, including the positive-zero-negative values, for the second-harmonic wave. We clarified that the observed enhancement results from high electron density in negative-permittivity plasma, the propagating fundamental frequency wave not being attenuated in the negative-refractive-index state, and partial phase matching between the fundamental and second-harmonic waves.