The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 1,3S) and He(2 1,3P), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1–0.5%. For interactions with other alkali-metal atoms the uncertainty is 1–3% in the coefficient C5, 1–5% in the coefficient C6, and 1–10% in the coefficients C8 and C10. The dispersion coefficients Cn for the interaction of He(2 1,3S) and He(2 1,3P) with the ground-state alkali-metal atoms and for the interaction of He(2 1,3S) with the alkali-metal atoms in their first 2P states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.