We present a novel approach to model and reconstruct radiance fields. Unlike NeRF that uses pure MLPs, we consider the full volume field as a 4D tensor and propose to factorize the tensor into multiple compact low-rank tensor components for efficient scene modeling. We model a scene (left) as a tensorial radiance field (right) using a set of vectors and matrices that describe scene appearance and geometry along their corresponding axes. These vector/matrix factors are used to compute volume density and view-dependent RGB color via vector-matrix outer products, leading to efficient radiance field reconstruction and realistic rendering. We demonstrate that TensoRF with CP decomposition can achieve fast reconstruction with better rendering quality and even a smaller model size ( 4MB) than NeRF.