Ionic polymer actuators driven by electrical stimuli have been widely investigated for use in practical applications such as bioinspired robots, sensors, and biomedical devices. However, conventional ionic polymer-metal composite actuators have a serious drawback of poor durability under long-term actuation in open air, mainly because of the leakage of the inner electrolyte and hydrated cations through cracks in the metallic electrodes. Here, we developed a highly durable and water-floatable ionic polymer artificial muscle by employing hydrophobic and asymmetrically laser-scribed reduced graphene oxide paper electrodes (HLrGOP). The highly conductive, flexible, and cost-effective HLrGOP electrodes have asymmetrically smooth hydrophobic outer and rough inner surfaces, resulting in liquid-impermeable and water-floatable functionalities and strong bonding between an ionic polymer and the electrodes. More interestingly, the HLrGOP electrode, which has a unique functionality to prevent the leakage of the vaporized or liquid electrolyte and mobile ions during electrical stimuli, greatly contributes to an exceptionally durable ionic polymer-graphene composite actuator that is a prerequisite for practical applications in active biomedical devices, biomimetic robots, touch-feedback haptic systems, and flexible soft electronics.