Atomic details of the dramatic increase in the diffusional growth rate of A15 Nb₃Sn superconducting compound with Ti addition have been investigated using atomistic simulations and experimental observations. Ti atoms preferentially locate at Nb sites in the Nb₃Sn bulk while they do not affect the volume diffusion of Sn significantly. In addition, Ti is predicted to segregate on Nb₃Sn grain boundaries, inducing the segregation of Sn, but cannot enhance the grain boundary diffusion of Sn enough to explain the dramatic increase in the growth rate of the Nb₃Sn layer. On the other hand, grain refinement is observed when Ti is added, which is expected to substantially promote the effective diffusion of Sn. Consequently, grain refinement due to the grain boundary segregation of Ti is revealed as the most important mechanism underlying the alloying effect of Ti. A basic understanding of the atomic behavior of alloying elements in Nb₃Sn and clarified alloying effects on the diffusional growth of Nb₃Sn compounds will contribute to further investigation of optimal alloying strategies.