The magnetic plasmon (MP) modes in the metal-dielectric-metal nanosandwich structure are investigated numerically, and the principle of energy resonance in such a resonator is proposed. An equivalent inductance capacitance circuit analysis method is proposed and the results are in agreement with the numerical simulations. Based on the MP resonance in such a structure, a nanosandwich chain waveguide is designed. Gold and silver are chosen as the metal materials. The power transmission efficiency of the nanosandwich waveguide can be as high as 0.546 in a specific nanosandwich unit cell, even when the metal absorption loss is large, which is the perspective of the new waveguides and lasers based on MP modes.