Based on the results of study on conventional rigid support nonlinear energy harvesters, in this paper, we conceive a kind of structure with an elastic-supported external magnet, for keeping the system in a state of bistable oscillation due to low-intensity excitations. Thus, an efficient electromechanical energy conversion can be accomplished. Studies show that the elastic-supported nonlinear energy harvesting systems do not need real-time adjustment of magnet spacings to meet varying-intensity random excitation vibrations. This structure helps to better satisfy the variable-intensity random excitation source, consequently it achieves efficiently electromechanical energy conversion.