Although supported bimetallic nanoparticles (Au-Pd NPs) demonstrate outstanding efficiency, challenges appear for carbon supported small and stable bimetallic nanoparticles used in liquid-phase reactions. In this work, Au-Pd NPs were supported on two types of carbon nanotubes: CNTs decorated covalently with carboxylic acid groups (O-CNTs) and non-covalently with the conductive poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) polymer (P-CNTs). The Au-Pd NPs were prepared using the sol immobilization approach on the functionalized CNTs, and the effect of the utilized functionalization method on the properties of the immobilized metallic nanoparticles and the performance of the nanocomposite catalysts was investigated. The fabricated nanocomposites were characterized using Fourier-transform infrared spectroscopy (FTIR), Raman spectroscopy, High-resolution transmission electron microscopy (HRTEM) and scanning electron microscopy (SEM). The catalytic performance of Au-Pd/O-CNTs and Au-Pd/P-CNTs was exploited for the oxidation of both cyclooctene and benzyl alcohol. Oxidation and polymer decoration directly led to an enhancement in the performance of CNTs catalysts. The nanocomposite catalyst with oxidized CNTs (Au-Pd/O-CNTs) was also found to be much more efficient and robust than that with polymer decorated CNTs (Au-Pd/P-CNTs). The enhancement in the oxidation of both cyclooctene and benzyl alcohol on Au-Pd/O-CNTs is attributed to the well-dispersed and smaller Au-Pd NPs as active sites on the surface of O-CNTs as compared to the P-CNTs surface.