Recently, metal-organic frameworks (MOFs) have attracted great interest in energy storage areas. However, the poor structural stability of MOFs derived from weak coordination bonds limits their applications. Here, quadruple hydrogen bonds (H-bonds) were introduced onto the MOFs to enhance their structural stability. Cross-linked networks could be formed between molecules owing to multiple H-bonds, strengthening the framework stability. Moreover, the dynamic reversibility of H-bonds could endow MOFs with self-healing ability. Furthermore, due to lower binding energy compared to coordination bonds, H-bonds break preferentially when subjected to internal stress, thus protecting the MOFs. Consequently, the as-prepared self-healing hybrid (SHH-Cu-MOF@Ti3C2TX) exhibited high capacitance retention (89.4%) after 5000 cycles at 1 A g-1, while that hybrid without dynamic H-bonds (H-Cu-MOF@Ti3C2TX) presented a 79.9% retention, delivering an enhancement in cycling stability. Moreover, an asymmetric supercapacitor (ASC) was fabricated by employing SHH-Cu-MOF@Ti3C2TX and activated carbon (AC) as the electrodes. The ASC delivered a specific capacitance (47.4 F g-1 at 1 A g-1), an energy density (16.9 Wh kg-1), and a power density (800 W kg-1) as well as good rate ability (retains 81% of its initial capacitance from 0.2 A g-1 to 5 A g-1).