Flexible supercapacitors that maintain electrochemical performance under deformation have attracted much attention for the potential application in the flexible electronics market. A compressible and flexible free-standing electrodes sponge and all-solid-state symmetric supercapacitors based on as prepared electrodes are presented. The carbon nanotubes (CNTs) framework is synthesized by chemical vapor deposition (CVD) method, and then composited with poly (3,4-ethylenedioxythiophene) PEDOT by the electrodeposition. This CNTs/PEDOT sponge electrode shows highest mass-specific capacitance of 147 Fg(-1) at 0.5 A g(-1), tuned by the PEDOT mass loading, and exhibits good cyclic stability with the evidence that more than 95% of capacitance is remained after 3000 cycles. Furthermore, the symmetric supercapacitor shows the highest energy density of 12.6 Wh kg(-1) under the power density of 1 kW kg(-1) and highest power density of 10.2 kW kg(-1) with energy density of 8 Wh kg(-1), which exhibits both high energy density and power density. The electrochemical performance of composite electrode also indicates that the operate voltage of device could be extend to 1.4 V by the n-doping and p-doping process in different potential of PEDOT component. This flexible supercapacitor maintains stable electrochemical performance working on different bending condition, which shows promising prospect for wearable energy storage applications. (C) 2017 Elsevier B.V. All rights reserved.