A biaxially wave-shaped polydimethylsiloxane (PDMS) surface was developed simply by using a taro leaf as the template. The resulting leaf-templated PDMS (L-PDMS) possesses a micro-sized curved interface structure, which is greatly beneficial for the exact embedding of a silver nanowire (AgNW) network conductive film covering the L-PDMS surface. The intrinsically curved AgNW/L-PDMS film surface, without any dangling nanowire, could prevent the fracture of AgNWs due to stretching stress even after cyclic stretching. More importantly, it also exhibited a biaxial stretchability, which showed ultra-stable resistance after continuous stretching for 100 cycles each in X- and Y-directions. This biaxially stretchable AgNW/L-PDMS film could extend the application fields in stretchable electronics.