We report here the development of an actuator with an ionic electromechanically active polymer (IEAP) laminate that is exclusively designed to exhibit a combination of high electrically induced strain and high bending modulus. The newly constructed laminate is one of the few IEAPs meeting the requirements for use in miniature soft robotics. The laminate has activated carbon-based electrodes and ionic liquid is used as an electrolyte. Layers of compliant gold foil are used as current collectors. The superior performance of the IEAP laminate is demonstrated by constructing a centimeter-scale robot propelled by a single IEAP actuator. The cyclic locomotion of the robot is inspired by the movements of an inchworm, while the IEAP laminate is used concurrently as an actuator and a structural member. The 830-mg robot is able to crawl on a smooth surface in open air, solely by undulation of its body. The microprocessor-controlled robot has an on-board lithium battery and uses a pulse-width-modulated signal to drive the IEAP actuator. The robot is able to carry its own power supply and even an extra payload. The constructed biomimetic robot is distinctive for the use of a non-planar actuator whose shape is programmed during the manufacturing process.