The previously reported gel and polymer actuators require external inputs, such as batteries, circuits, electronic circuits, etc., compared with autonomous motions produced by the living organisms. To realize the spontaneous motions, here, we propose to integrate a power supply, actuators, and control into a single-component self-oscillating hydrogel. We demonstrate self-actuating gel pumps driven by the oscillatory Belousov-Zhabotinsky (BZ) reaction without electronic components. We have developed the volume oscillation of gels synchronized with the BZ reaction (BZ gel). Since the self-actuating gel pumps are driven by chemo-mechanical energy from BZ gels, the self-actuating gel pumps don't require complex wiring designs, energy supply, and assembling. The mechanical work generated by BZ gels is extremely small. We formulated the thermodynamic cycle of BZ gels and maximized mechanical work. We found that pre-stretched BZ gel shows larger mechanical works. We physically separated the BZ gels and working fluid to create practical pumps. By using optimizing mechanical generated by BZ gels, we demonstrated the self-actuating gel pumps that transfer mechanical work through a stretchable elastomer membrane.