We numerically present that suppressing the unwanted resonance mode in a metal-insulator-metal (MIM) structure can be achieved by using a fine-structured gold grating. In each period of the grating, a sub-grating consisting of multiple gold strips is used. Investigations on a high quality-factor (Q-factor) MIM structure with the grating and usual gratings are carried out. Comparisons show that the proposed grating supports different diffraction orders. Moreover, the unwanted mode which exists in the case of usual gratings can be significantly suppressed, and the desired mode can be kept almost unchanged. Thus, the MIM structure with our grating shows a single resonance at ~3.9 μm with a high Q-factor (~260) and an ultra-narrow linewidth (~10 cm-1) over a broad spectral region. This study provides a simple and effective approach to selective manipulating the resonance modes in MIM structures, which is useful for design of mid-infrared narrowband filters, emitters, and absorbers.