The magnetic plasmon (MP) modes in metal-dielectric-metal nanosandwich structures are investigated numerically using finite-difference time-domain method. We demonstrate the law of the quality factor in this kind of resonator.According to the MP modes in the nanosandwich structures, we design a series of resonators of this kind in order to investigate how to tune the resonante frequencies of MP modes through tuning the geometrical parameters and the dielectric layer refractive index of resonators, and the obtained result is well consonant with our analysis by the equivalent inductance capacitance circuit. We also investigate the electromagnetic energy confinement of the nanosandwich resonators, and analyse the Q factors of these structures from thermal and radiant points of view, which will guide one in designing new waveguides and lasers based on MP modes.