Herein, we report a cost-effective and easy synthetic procedure for the fabrication of a graphene-single-walled carbon nanotube-poly(3-methylthiophene) ternary nanocomposite for high-performance supercapacitor electrodes. The possible interactions of both graphene (Gr) and single-walled carbon nanotubes (SWCNTs) with poly(3-methylthiophene) (PMT) were characterized by Fourier transform infrared, UV-visible, and Raman spectroscopies. A morphological study confirmed the formation of a bridge between PMT-coated SWCNTs and Gr layers. The ternary nanocomposite showed superior electrical conductivity of 4.68 S/cm at room temperature and also exhibited nonlinear current voltage characteristics. The ternary nanocomposite achieved a maximum specific capacitance of 561 F/g at a 5 mV/s scan rate. Both a high energy density and a high power density were obtained for the ternary nanocomposite. Here, both the Gr and SWCNTs take part in the increment of the electrochemical properties. A higher thermal stability was also observed for the ternary nanocomposite. Based on its outstanding properties, the ternary nanocomposite is a potential candidate for a high-performance supercapacitor electrode.