Stimuli-responsive polymers and their application to biomaterials have been widely studied. On the other hand, as a novel biomimetic polymer, we have been studying the polymer with an autonomous self-oscillating function by utilizing oscillating chemical reactions. So far, we succeeded in developing a novel self-oscillating polymer and gels by utilizing the oscillating reaction, called the Belousov-Zhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. The self-oscillating polymer is composed of poly(N-isopropylacrylamide) (PNIPAAm) network in which the catalyst for the BZ reaction is covalently immobilized. Under the coexistence of the reactants, the polymer undergoes spontaneous cyclic soluble-insoluble changes or swelling-deswelling changes (in the case of gel) without any on-off switching of external stimuli. In this paper, our recent studies on the self-oscillating polymer gels and the design of functional material systems using the polymer are summarized.