In the present investigation, in situ green reduction approach is used to uniformly decorate the Ag-Au bimetallic nanoparticles (BNPs) on the surface of acid functionalised multi-walled carbon nanotubes (MWCNTs). The adsorbed Terminalia catappa aqueous leaf extract biopolymers on the surface of MWCNTs can increase the in situ reduction of Ag, Au ions to Ag-Au BNPs and stabilise them which can operate as a capper/stabiliser and reductant agent. X-ray diffraction (XRD), high-resolution transmission electron microscopy (HR-TEM), scanning electron microscopy - energy dispersive x-ray spectroscopy (SEM-EDX), Fourier-transform infrared spectroscopy (FT-IR) and UV–visible spectroscopy techniques were employed to examine the structures, morphologies, composition, chemical bonds and optical properties of the functionalised MWCNTs and the nanohybrid. The results revealed that the spherical T.C-Ag-Au bimetallic nanoparticle with average size 12.4 nm was uniformly distributed on the surface of modified MWCNTs. Finally, evaluation of the catalytic activity of the T.C-Ag-Au BNPs decorated MWCNTs exhibited excellent catalytic performance for completing the reduction of 4-Nitrophenol (4-NP) and degradation of alizarin red (AR) dye at ambient temperature with a great rate constant and the degradation efficiency of 98.7% and 96.4%, respectively. The order of reaction, rate constant, half-life and mechanism of catalytic activity of the T.C-Ag-Au BNPs@COOH-MWCNTs nanohybrid were calculated using the Langmuir–Hinshelwood model. The catalyst can be retained and reapplied eight times without affecting its catalytic performance. The interaction between T.C-Ag-Au BNPs and MWCNTs has a synergistic effect, which is accountable for the enhanced catalytic activity.