Annivite-(Zn), Cu6(Cu4Zn2)Σ6Bi4S13, is a new IMA-approved mineral species from the Geister vein, Jáchymov ore district, Czech Republic. It occurs as anhedral grains, up to 50 μm in size, and growth zones, up to 100 μm in thickness, hosted by oscillatory zoned annivite-(Zn)/tennantite-(Zn) grains, and associated with Bi-rich tennantite-(Zn), tennantite-(Fe), tetrahedrite-(Zn), the not-yet approved ‘annivite-(Fe)’, bismuth, emplectite, wittichenite and supergene bismite, walpurgite and metazeunerite. In reflected light, annivite-(Zn) is isotropic, pale grey with a brownish shade and very rare pale brown internal reflections. Reflectance data for the four COM wavelengths in air are [λ (nm): R (%)]: 470: 32.3; 546: 32.0; 589: 32.0; 650: 31.6. Electron microprobe analysis gave (in wt.% – average of 5 spot analyses): Cu 36.29, Ag 0.14, Fe 0.08, Zn 7.11, Pb 0.19, As 6.07, Sb 4.50, Bi 21.08, S 23.68, total 99.14. On the basis of ΣMe =16 atoms per formula unit, the empirical formula of annivite-(Zn) is Cu10.13Ag0.02Zn1.93Fe0.03Pb0.02Bi1.79As1.43Sb0.66S13.10. Annivite-(Zn) is cubic, I$\bar 4$3m, with unit-cell parameters a = 10.3545(6) Å, V = 1110.16(19) Å3 and Z = 2. Its crystal structure was refined by single-crystal X-ray diffraction data to a final R1 = 0.0493 on the basis of 278 unique reflections with Fo > 4σ(Fo) and 23 refined parameters. Annivite-(Zn) is isotypic with other tetrahedrite-group minerals. Its crystal chemistry is discussed, and previous findings of Bi-rich tetrahedrite-group minerals are briefly reviewed, along with the description of a second finding of annivite-(Zn) from the abandoned Mauritius tin mine, Hřebečná, Krušné hory Mountains, Czech Republic.