Enhancement of light absorption in two-dimensional (2D) single atomic layer materials is a significant issue for applications of 2D material-based optoelectronic devices. In this letter, the dual-band enhanced absorptions in monolayer transition-metal dichalcogenides (TMDs) are obtained based on the metmaterial nanostructures. The proposed nanostructure consists of a monolayer TMDs sandwiched between Ag nanodisks and a dielectric spacer on Ag substrate. The excitations of the surface plasmon polaritons (SPPs) and the magnetic dipole resonances contribute to the high absorption efficiency, and the resulting absorption enhancement can be separately tuned by simply adjusting the structural parameters such as the spacer thickness, the size and the period of the Ag nanodisks. In addition, a hybrid nanostructure consisting of different nanodisks can increase the absorption bandwidth. The calculated results may have some potential applications in photodetection and wavelength-selective photoluminescence.