The dispersion relation and gain spectra of modulation instability (MI) are analytically deduced in negative-index materials by directly starting from the extended nonlinear propagation equation including saturable nonlinearity and higher-order dispersion and by adopting the linear stability analysis and Drode electromagnetic model. And the variations of the equation coefficients with the normalized angular frequencies are calculated in real units for future experimental demonstrations. Then the variations of the gain spectra with the normalized angular frequencies and normalized optical intensities are also calculated and discussed in real units. The results show that, when the normalized angular frequencies are fixed, with the increasing normalized optical intensities, the cut-off frequencies and peak gains of MI will increase before decrease. And the cut-off frequencies and peak gains are different for different normalized angular frequencies. Moreover, the gain spectra will depart far away from the zero point when the normalized angular frequencies are close to the forbidden band region. When the normalized optical intensities are fixed, the cut-off frequencies and peak gains increase with the normalized angular frequencies. And when the normalized angular frequency increases to be close to the forbidden band region, the gain spectrum will shift far away from the zero point.