By considering a spin bias in the source of a three-terminal triple-quantum-dot ring, the electron transport properties in such a structure are studied. We find that the spin-bias-driven charge and spin currents in the two drains are strongly dependent on the quantum interference in this structure. From investigating the spin accumulations in the quantum dots, the electron transport induced by spin bias is described clearly. Moreover, we see that the level characteristic of the quantum dot coupled to the source terminal influences the electron transport nontrivially. The many-body effect is taken into account within the Hubbard-I approximation, we then find that it plays a unique role in modifying the charge and spin transport through this structure.