A biomimetic jellyfish robot based on ionic polymer metal composite actuators was fabricated and activated to mimic real locomotive behavior with pulse and recovery processes. To imitate the curved shape of the jellyfish, a thermal treatment was applied to obtain a permanent initial deformation of a hemispherical form. The bio-inspired input signal was generated for mimicking real locomotion of the jellyfish. The vertical floating displacement and the thrust force of the biomimetic jellyfish robot under various input signals were measured and compared. The present results show that the bio-inspired electrical input signal with pulse-recovery process generates much higher floating velocity of the biomimetic jellyfish robot in comparison with pure sinusoidal excitations. The curved shape of the IPMC actuator through thermal treatments can be successfully applied to mimic the real biomimetic robots with smooth curves.