Low-frequency wideband noise reduction has posed a significant problem to the scientific and technical communities in recent years. A single layer of a parallel-arranged inhomogeneous micro-perforated panel (iMPP) coupled with spider-web designed cavities is offered as a composite acoustic structure in this paper. Three different spider-web shapes have been designed and studied, i.e. circular, octagonal, and square. By controlling the different inhomogeneous patterns, perforation ratio, the thickness of iMPP, and back cavity depths, a broader multipeak low-frequency sound-absorbing performance equivalent to different resonant frequencies can be achieved. To anticipate the sound absorption coefficient of the new design, both theoretical analysis and finite-element method (FEM) simulation are executed. The predicted and FEM simulation sound absorption results of the new composite structure are verified in the experimental investigation using a square-designed sound impedance tube. By a subwavelength thickness of just 100 mm, a highly effective low-frequency broadband sound-absorbing composite structure is successfully attained by integrating many inhomogeneous MPP unit cells supported with spider-web-designed cavities. The average sound absorption coefficient is over 90% ( α = 0.94) within the bandgap of 230 Hz to 470 Hz. Compared to traditional sound-absorbing materials, the composite structure comprises inhomogeneous MPP coupled with spider-web-designed cavities, which may provide good absorption performance while maintaining a modest and robust construction for active low-frequency noise suppression.