Inspired by the brick-mortar structure, multi-functional thermoplastic polyurethane (TPU) composites with carbon nanostructures (CNS), (branched carbon nanotubes) were fabricated via an interface-designed network strategy. This strategy enables obtaining conductive networks within the TPU matrix at low filler percolation threshold of 0.06 wt. % in a facile and environmentally-friendly way. For example the TPU composite with 0.7 wt. % CNS has high electrical conductivity up to 1 S/m. Moreover this composite shows elongation at break as high as 930% and excellent piezoresistive sensitivity (gauge factor up to 6861) at high-level strains (e.g. 660%). Tunable electrical conductivity, piezoresistive and mechanical properties can be achieved by changing the CNS content. These composites are very promising for the fabrication of strain sensors with excellent stretchability and high piezoresistive sensitivity.