Although fossil evidence suggests the existence of an early muscular system in the ancient cnidarian jellyfish from the early Cambrian Kuanchuanpu biota (ca. 535 Ma), south China, the mechanisms underlying the feeding and respiration of the early jellyfish are conjectural. Recently, the polyp inside the periderm of olivooids was demonstrated to be a calyx-like structure, most likely bearing short tentacles and bundles of coronal muscles at the edge of the calyx, thus presumably contributing to feeding and respiration. Here, we simulate the contraction and expansion of the microscopic periderm-bearing olivooid Quadrapyrgites via the fluid-structure interaction computational fluid dynamics (CFD) method to investigate their feeding and respiratory activities. The simulations show that the rate of water inhalation by the polyp subumbrella is positively correlated with the rate of contraction and expansion of the coronal muscles, consistent with the previous feeding and respiration hypothesis. The dynamic simulations also show that the frequent inhalation/exhalation of water through the periderm polyp expansion/contraction conducted by the muscular system of Quadrapyrgites most likely represents the ancestral feeding and respiration patterns of Cambrian sedentary medusozoans that predated the rhythmic jet-propelled swimming of the modern jellyfish. Most importantly for these Cambrian microscopic sedentary medusozoans, the increase of body size and stronger capacity of muscle contraction may have been indispensable in the stepwise evolution of active feeding and subsequent swimming in a higher flow (or higher Reynolds number) environment.