Conventional power sources encounter difficulties in achieving structural unitization with complex-shaped electronic devices because of their fixed form factors. Here, it is realized that an on-demand conformal Zn-ion battery (ZIB) on non-developable surfaces uses direct ink writing (DIW)-based nonplanar 3D printing. First, ZIB component (manganese oxide-based cathode, Zn powder-based anode, and UV-curable gel composite electrolyte) inks are designed to regulate their colloidal interactions to fulfill the rheological requirements of nonplanar 3D printing, and establish bi-percolating ion/electron conduction pathways, thereby enabling geometrical synchronization with non-developable surfaces, and ensuring reliable electrochemical performance. The ZIB component inks are conformally printed on arbitrary curvilinear substrates to produce embodied ZIBs that can be seamlessly integrated with complicated 3D objects (including human ears). The conformal ZIB exhibits a high fill factor (i.e., areal coverage of cells on underlying substrates, ≈100%) that ensures high volumetric energy density (50.5 mWh cm cell −3), which exceeds those of previously-reported shape-adaptable power sources.