The combination of critical coupling and coupled mode theory in this study elevated the absorption performance of a graphene-based absorber in the near-infrared band, achieving perfect absorption in the double bands (98.96% and 98.22%), owing to the guided mode resonance (the coupling of the leak mode and guided mode under the condition of phase matching, which revealed 100% transmission or reflection efficiency in the wavelet band), and a third high-efficiency absorption (91.34%) emerged. During the evaluation of the single-structure, cross-circle-shaped absorber via simulation and theoretical analysis, the cross-circle shaped absorber assumed a conspicuous preponderance through exploring the correlation between absorption and tunable parameters (period, geometric measure, and incident angle of the cross-circle absorber), and by briefly analyzing the quality factors and universal applicability. Hence, the cross-circle resonance structure provides novel potential for the design of a dual-band unpatterned graphene perfect absorber in the near-infrared band, and possesses practical application significance in photoelectric detectors, modulators, optical switching, and numerous other photoelectric devices.