Pumps are critical life-sustaining components for all animals. At the earliest stages of life, the tubular embryonic heart works as a valveless pump capable of generating unidirectional blood flow. Inspired by this elementary pump, we developed an example of a biohybrid valveless pump-bot powered by engineered skeletal muscle. Our pump-bot consists of a soft hydrogel tube connected at both ends to a stiffer polydimethylsiloxane (PDMS) scaffold, creating an impedance mismatch. A contractile muscle ring wraps around the hydrogel tube at an off-center location, squeezing the tube with or without buckling it locally. Cyclic muscle contractions, spontaneous or electrically stimulated, further squeeze the tube, resulting in elastic waves that propagate along the soft tube and get reflected back at the soft/stiff tube boundaries. Asymmetric placement of muscle ring results in a time delay between the wave arrivals, thus establishing a net unidirectional fluid flow irrespective of whether the tube is buckled or not. Flow rates of up to 22.5 μL/min are achieved by the present pump-bot, which are at least three orders of magnitude higher than those from cardiomyocyte-powered valve pumps of similar size. Owning to its simple geometry, robustness, ease of fabrication, and high pumping performance, our pump-bot is particularly well-suited for a wide range of biomedical applications in microfluidics, drug delivery, biomedical devices, cardiovascular pumping system, and more.