This study constructs a flexible, high-performance, quasi-solid-state, asymmetric supercapacitor (ASC) consisting of a positive electrode of Na+-pre-inserted MnO2 deposited-carbon nanotubes (NaxMnO2@CNT), potassium poly(acrylate) cross-linked water-born polyurethane (WPU-PAAK) gel polymer electrolyte soaked with 1 M Na2SO4, and activated carbon-CNT (AC-CNT) composite (NaxMnO2@CNT/ WPU-PAAK-Na2SO4/AC-CNT). The pre-insertion of Na+ enhances the utilization of delta-phase MnO2 and the usage of carbon nanotubes (CNTs) is beneficial to promote the electronic conductivity, achieving the optimal performance of NaxMnO2@CNT with high specific capacitance of 230 and 130 F g(-1) at 1 and 20 A g(-1) in the designed gel polymer electrolyte, WPU-PAAK-Na2SO4. The specific capacitance of the ACCNT composite is also optimized to achieve the high specific capacitance of 180 and 127 F g(-1) at 1 and 20 A g(-1) in the same gel electrolyte. This quasi-solid-state ASC with a high cell voltage of 1.8 V can deliver a high cell capacitance, large specific energy, and good specific power of 36.8 F g(-1), 16.38 Wh kg(-1) and 1.04 kW kg(-1), respectively, at 1 A g(-1). This ASC also provides an outstanding area-based cell capacitance, areal energy density and areal power density of 254.4 mF cm(-2) , 111.92 mu Wh cm(-2) and 10.35 mW cm(-2), respectively. This highly flexible ASC with 93.4% cell capacitance retention at a bending angle of 180 degrees exhibits an excellent cycle life (97% capacitance retention in a 10,000-cycle test). (C) 2019 Elsevier Ltd. All rights reserved.