A carbon nanotube (CNT) sponge contains a three-dimensional conductive nanotube network, and can be used as a porous electrode for various energy devices. We present here a rational strategy to fabricate a unique CNT@polypyrrole (PPy) core–shell sponge, and demonstrate its application as a highly compressible supercapacitor electrode with high performance. A PPy layer with optimal thickness was coated uniformly on individual CNTs and inter-CNT contact points by electrochemical deposition and crosslinking of pyrrole monomers, resulting in a core–shell configuration. The PPy coating significantly improves specific capacitance of the CNT sponge to above 300 F/g, and simultaneously reinforces the porous structure to achieve better strength and fully elastic structural recovery after compression. The CNT@PPy sponge can sustain 1, 000 compression cycles at a strain of 50% while maintaining a stable capacitance (> 90% of initial value). Our CNT@PPy core–shell sponges with a highly porous network structure may serve as compressible, robust electrodes for supercapacitors and many other energy devices.