High-performance energy storage device is rapidly developing to meet product demands for portable and wearable electronic products. Here, ZnCo₂O₄ coated on nickel foam (NF) prepared by hydrothermal method is used as the anode for supercapacitors, revealing a specific capacity (92.22 mAh g⁻¹) and a repeatable rate of performance. Furthermore, an alkyne hydrogel electrolyte (PVA/CMC/KOH) based on polyvinyl alcohol (PVA) and carboxymethyl cellulose (CMC) is constructed, and the hydrogel containing 0.1 g CMC exhibits excellent ionic conductivity (13.33 S m⁻¹) for quick charge transfer and adequate ion transport. Considering these advantageous characteristics, a quasi-solid-state hybrid supercapacitor fabricating with ZnCo₂O₄, activated carbon (AC), and PVA/CMC-0.1 delivers a maximum energy density of 17.99 Wh kg⁻¹ at a power density of 800 W kg⁻¹, and the capacity retention rate is about 54.95% after 5000 cycles at 5 A g⁻¹. The deterioration in cyclic characteristics mostly happen in the first 1000 cycles, which may attribute to the loss of the infiltrated KOH solution in the gel during the process of rapid charging and discharging in the starting period. After that, the cyclic characteristics become stabilized in the following cycling procedure. Furthermore, the ZnCo₂O₄//PVA/CMC-0.1//AC quasi-solid-state supercapacitor can maintain its performance under different bending angles, which provides a new possibility for the application of supercapacitors in flexible devices.