The cross section for one-electron transfer H − + He + → H(1s) + He * (1s, nlm) is calculated in this paper. The collisional system is treated as a three-electron one and matrix elements for the formation of excited helium He * (1s, nlm) in both singlet and triplet states (1S, 2 1,3 S, P and 3 1,3 S, P, D) are obtained. Close-coupling calculations were done for the 27 1s, nlm| (1S, 2 1,3 S, P and 3 1,3 S, P, D) final states covering the range 1-10 × 10 7 cm s −1 of the relative collision velocity. An approximation is used for the effective potential of H − and Coulomb Green's functions are used to describe the weakly bound electron of H − . A satisfactory agreement is obtained with the experimental cross section.