<p>An acoustic liner is used in combustion ducts and aeroengine nacelles to reduce noise. In the afterburner of a high-thrust-producing gas turbine engine, an acoustic liner in the presence of a simultaneous grazing flow and a bias flow mitigates thermoacoustic instability, a phenomenon in which pressure oscillations from combustion interact with acoustic waves, leading to undesirable vibrations and increased tonal noise. Using an acoustic liner prevents the feedback loop between heat release and pressure fluctuations. In most applications, acoustic liners are cylindrical with uniform cross-sectional area. In an attempt to enhance sound absorption, this paper presents an experimental investigation into the acoustic attenuation characteristics of conical-cavity-backed conical perforated liners in the presence of simultaneous bias and grazing flows. Several combinations of cone angles of liners and cavities are designed and fabricated, and a parametric study of cone angles is conducted for the no-flow and combined grazing–bias flow cases. The acoustic attenuation ability of conical liners and cavities is compared with their cylindrical counterparts. The experimental setup involves subjecting liners to controlled bias and grazing flow conditions and measuring their acoustic performance using the impedance tube technique. Conical adapters are used for conical liners to match the impedance tube diameter. The sound absorption coefficient of cavity-backed liners is calculated using the ASTM two-load method. Numerical simulations are performed by solving linearized Navier–Stokes equations in the frequency domain using COMSOL Multiphysics. Sound absorption coefficients obtained numerically are then compared with those of experimental measurements. Experimental results demonstrate that conical lined ducts provide better sound absorption than cylindrical lined ducts at specific grazing and bias flow rates.</p>