Recent studies of the generation of large-scale fluctuations by the drift-Alfvèn modes or by the drift-tearing modes adopt the negative-viscosity plasmas that model the effect of small-scale turbulence. With the turbulence assumed to be a Gaussian random noise of power-law spectrum, the renormalization-group method is applied in order to explore the large-scale dynamics of the noise-driven magnetohydrodynamic plasma with negative viscosity in the long-time limit. The viscosity, the resistivity, the magnetic field and the strength of the noise are renormalized by regularizing the divergent response functions, the noise and the couplings. The ratio of the resistivity to the viscosity and the strength of the noise are obtained. Based on the anomalous dimensions of the velocity and the magnetic field, it is shown that the kinetic energy spectrum is steeper than the magnetic energy due to the renormalization of the Lorentz force, which is opposite to the case of positive viscosity.