A pure spin current of a triplet exciton has been proposed for a threedimensional system based on Dirac relativistic quantum mechanics, considering spin to be an intrinsic relativistic quantum variable. The transport dissipations of the triplet exciton caused by the magnetic excitation and the Coulomb interaction (such as the bremsstrahlung effect) can be minimized, making it possible to produce a pure exciton spin current with minimized charge-induced dissipation for the transport of information in spin-based devices. The exciton spin current can be expressed as a sum of an electron spin current and a hole spin current, modulated by an envelope function. It flows along the tangential direction of the isodense of the exciton. Both external electric and magnetic fields influence the exciton spin current and can be used to separate the triplet exciton and the singlet exciton. A simplification of our model, i.e., considering only an external electric field, yields the same result reported by Shen (2005 Phys. Rev. Lett. 95 187203), in which the spin current was phenomenologically derived by the expectation value of the product of spin and velocity observables. Incorporation and possible application of the exciton spin current in several systems are discussed.Spintronics is a subdiscipline of condensed matter physics whose main aim is to control and manipulate the electronic spin degree of freedom. The primary attention focuses on the basic physical principles underlying the spin injection, spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals [1][2][3]. Many proposed spintronic device schemes turn out to be practical eventually. At present, spin injection has been successfully realized in diluted magnetic semiconductors (DMSs) [4,5]. Nevertheless, the Curie temperature of the DMSs is still low and unstable for practical use at room temperature. Apart from the DMSs that make use of both the charge and spin of electrons to process and