A fundamental challenge in neuroscience is to connect the neural mechanisms with behavior. Networks that produce rhythmic motor behaviors, such as locomotion, provide important model systems to address this problem. A particularly good model for this purpose is the neural circuit underlying the coordinated rhythmic limb movements in the crayfish swimmeret system. During forward swimming, rhythmic movements of limbs on different segments of the crayfish abdomen progress from back to front with the same period, but neighboring limbs are phase-lagged by 25% of the period. We show that different network topologies of the neural circuit would produce robust phase constant rhythms of 0%, 25%, 50% or 75% phase-lag. However, only crayfish’s natural 25% back-to-front phase constant rhythm gives the most powerful and efficient swimming. Our results suggest that the particular asymmetric network topology in the natural neural circuit of the crayfish swimmeret system is likely the result of evolution in favor of more powerful and efficient swimming.