Bio-hybrid micro-swimmers, composed of biological entities integrated with synthetic constructs, actively transport cargo by converting chemical energy into mechanical work. Here, using isolated and demembranated flagella from green algae Chlamydomonas reinhardtii (C. reinhardtii), we build efficient axonemally-driven micro-swimmers that consume ATP to propel micron-sized beads. Depending on the calcium concentration, we observed two main classes of motion: whereas beads move along curved trajectories at calcium concentrations below 0.03 mM, they are propelled along straight paths when the calcium concentration increases. In this regime, they reached velocities of approximately 20 μm s-1, comparable to human sperm velocity in vivo. We relate this transition to the properties of beating axonemes, in particular the reduced static curvature with increasing calcium concentration. Our designed system has potential applications in the fabrication of synthetic micro-swimmers, and in particular, bio-actuated medical micro-robots for targeted drug delivery.