The characterization of quantum magnetism in a large spin (≥ 1) system naturally involves both spin-vectors and -tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spintensor (e.g., nematic in frustrated lattices) orders have been investigated separately, the coexistence and correlation between them have not been well explored. Here we propose and characterize a novel quantum spiral spin-tensor order on a spin-1 Heisenberg chain subject to a spiral spin-tensor Zeeman field, which can be experimentally realized using a Raman-dressed cold atom optical lattice. Through numerical density-matrix renormalization group (DMRG) simulation, we obtain the phase diagram and characterize the coexistence of spin-vector and spin-tensor orders as well as their correlations. Our results may open an avenue for exploring novel magnetic orders and spin-tensor electronics/atomtronics in large-spin systems.