In this paper a concept of a swimming robot is proposed inspired by the Anomalocaris, designed to explore the Europa's under-ice ocean where extraterrestrial life may exist. Anomalocaris is known as the largest ancient predator in the middle Cambrian. Unlike many sea fishes, Anomalocaris is considered as arthropod, which has a simpler body structure than vertebrate. It is likely to have an excellent swimming performance in the pristine ocean. A model for thrust calculation based on the reactive force generated by the fluid on its moving body is utilized in this work. First, the efficiency of two different edge contours are compared and some important relations representing the swimming performance are analyzed by considering key parameters, including but not limited to the wave number, the generated mean thrust and swimming patterns. In particular, an interesting relationship is revealed between the wave number and the swimming efficiency. An optimal wave number is obtained corresponding to the maximum efficiency. In addition, numerical simulations regarding the swimming pattern are performed to show its influence on the swimming performance.