We theoretically investigate the thermoelectric properties in a tunneling-coupled parallel DQD-AB ring attached to one normal and one superconducting lead. The role of the intrinsic and extrinsic parameters in improving thermoelectric properties is discussed. The peak value of figure of merit near gap edges increases with the asymmetry parameter decreasing, particularly, when asymmetry parameter is less than 0.5, the figure of merit near gap edges rapidly rises. When the interdot coupling strengh is less than the superconducting gap the thermopower spectrum presents a single-platform structure. While when the interdot coupling strengh is larger than the gap, a double-platform structure appears in thermopower spectrum. Outside the gap the peak values of figure of merit might reach the order of 102. On the basis of optimizing internal parameters the thermoelectric conversion efficiency of the device can be further improved by appropriately matching the total magnetic flux and the flux difference between two subrings.