Cell motility is central to processes such as wound healing, immune cell surveillance, and embryonic development. Motility requires the conversion of chemical to mechanical energy. An active area of research is to create motile particles, such as microswimmers, using catalytic and enzymatic reactions. Here, autonomous motion is demonstrated in adhesive polymer-based protocells by incorporating and harnessing the energy production of an enzymatic reaction. Biotinylated polymer vesicles that encapsulate catalase, an enzyme which converts hydrogen peroxide to water and oxygen, are prepared and these vesicles are adhered weakly to avidin-coated surfaces. Upon addition of hydrogen peroxide, which diffuses across the membrane, catalase activity generates a differential impulsive force that enables the breakage and reformation of biotin-avidin bonds, leading to diffusive vesicle motion resembling random motility. The random motility requires catalase, increases with the concentration of hydrogen peroxide, and needs biotin-avidin adhesion. Thus, a protocellular mimetic of a motile cell.