Photothermoelectric (PTE) detectors can work in a broad band range without using a cooling unit and external bias and therefore have attracted intense research interest. However, the performance of PTE detectors constructed using traditional TE materials has been limited by their poor optical absorption and intrinsic brittleness. We report a flexible graded TE material comprised of Bi2Te3 nanocrystals adsorbed on a single-wall carbon nanotube (SWCNT) network, which has excellent flexibility, high photo-thermal conversion ability and good TE properties. Flexible PTE detectors were constructed, and had an ultrahigh responsivity of 0.71 V/W, a high peak detectivity up to 2.1 × 108 Jones, and a broad response band ranging from the infrared to the terahertz band. The excellent PTE performance of the detectors is attributed to the broadband optical absorption of SWCNTs, the high TE performance of Bi2Te3 nanocrystals, and the graded layer structure of the hybrid.