Spintronic phenomena to date have been established in magnets with collinear moments, where the spin injection through the spin Seebeck effect (SSE) is always along the out-of-plane direction. Here, we report the observation of a vector SSE in a noncollinear antiferromagnet (AF) LuFeO_{3}, where temperature gradient along the out-of-plane and also the in-plane directions can both inject a pure spin current and generate a voltage in the heavy metal via the inverse spin Hall effect (ISHE). We show that the thermovoltages are due to the magnetization from canted spins in LuFeO_{3}. Furthermore, in contrast to the challenges of generating, manipulating, and detecting spin current in collinear AFs, the vector SSE in LuFeO_{3} is readily viable in zero magnetic field and can be controlled by a small magnetic field of about 150 Oe at room temperature. The noncollinear AFs expand new realms for exploring spin phenomena and provide a new route to low-field antiferromagnetic spin caloritronics and magnonics.