Hybrid composites La2-xCoxCuO4 (x = 0, 0.1, 0.2, and 0.3) are prepared using one-step simple hydrothermal route as electrodes for supercapacitors. The effect of varying cobalt content on morphological, structural, and electrochemical properties has been explored using X-ray diffraction, scanning electron microscopy, and cyclic voltammetry, respectively. The structural parameters obtained by X-ray diffraction showed tetragonal phase of hybrid composite without any evident impurity phases. The analysis of morphological properties suggested a strong correlation with electrochemical properties, for instance, a relationship between fabric porous structures and electrochemically active sites for redox reactions and intercalation/de-intercalation processes. The hybrid composite electrodes demonstrated high specific capacitance of the order of 1304 F/g at 10 mV/s scan rate and exhibited decreasing trend on increasing scan rate. Hybrid composites were also tested for their ability as an electrode of high performance supercapacitors in different aqueous electrolytes, i. e, KOH, H2SO4, and Na2SO4 to optimize the best compatible electrolyte. The composite electrode material showed excellent cyclic stability and 98% capacitance retention for 1 A/g after 2000 cycles. The remarkable performance of hybrid composite electrode entails its potential for commercial applications of supercapacitors.