<p>The forced Mathieu–Duffing equation is a key model for describing nonlinear vibration behaviors of engineering systems, where superharmonic resonance often triggers destructive jumping and hysteresis to threaten structural integrity. To address this problem, the superharmonic resonance characteristics and time-delay feedback controllability of a fractional Mathieu–Duffing equation are investigated in the present paper. The multiple scale method is employed to derive the amplitude–frequency equations for second-order and third-order superharmonic resonances. Based on these equations, the amplitude–frequency characteristic curves under different system parameters are plotted, and the influence of each parameter on resonance amplitude and instability region is analyzed. Furthermore, a time-delay displacement feedback controller is designed to suppress superharmonic resonance, and the amplitude–frequency response equations of superharmonic resonance under control are further derived. Notably, a new phenomenon is discovered in this model, where the feedback control with the added cubic displacement control term is consistent with the feedback control with only a linear displacement control term. Time-history response analyses verify the validity of the theoretically derived time-delay control strategy.</p>