In this work, CoMoO4@NiMoO4·xH2O core-shell heterostructure electrode is directly grown on carbon fabric (CF) via a feasible hydrothermal procedure with CoMoO4 nanowires (NWs) as the core and NiMoO4 nanosheets (NSs) as the shell. This core-shell heterostructure could provide fast ion and electron transfer, a large number of active sites, and good strain accommodation. As a result, the CoMoO4@NiMoO4·xH2O electrode yields high-capacitance performance with a high specific capacitance of 1582 F g−1, good cycling stability with the capacitance retention of 97.1% after 3000 cycles and good rate capability. The electrode also shows excellent mechanical flexibility. Also, a flexible Fe2O3 nanorods/CF electrode with enhanced electrochemical performance was prepared. A solid-state asymmetric supercapacitor device is successfully fabricated by using flexible CoMoO4@NiMoO4·xH2O as the positive electrode and Fe2O3 as the negative electrode. The asymmetric supercapacitor with a maximum voltage of 1.6 V demonstrates high specific energy (41.8 Wh kg−1 at 700 W kg−1), high power density (12000 W kg−1 at 26.7 Wh kg−1), and excellent cycle ability with the capacitance retention of 89.3% after 5000 cycles (at the current density of 3A g−1).