Stretchability and compressibility are essential features for next-generation flexible energy storage devices. Most previous studies on stretchable and compressible energy storage devices have focused on supercapacitors, whereas the intrinsically stretchable and compressible batteries are rarely reported for the lack of a stretchable and compressible high-performance electrolyte as well as highly conductive flexible electrodes. Here, a new type of intrinsically stretchable and compressible battery is fabricated for the first time, by employing a sodium polyacrylate (PANa) hydrogel as electrolyte, and nickel cobalt hydroxide and zinc nanosheets deposited on Au@CNT papers as electrodes. The newly developed battery can be intrinsically stretched up to 400% strain (capacity enhanced) and compressed to 50% strain (capacity well retained). After being stretched for 500 cycles and compressed for 1500 cycles, the battery is able to deliver 87% and 97% of its initial capacity, respectively.