We report on photoluminescence studies of Tb3+ in a polycrystalline cryolite type K3YF6 host. The location of the Tb3+ in the center of inversion forbids the electric-dipole transitions of terbium ions in this material. As a consequence almost the entire luminescence intensity is related to the 5D4-(7)F5 magnetic-dipole transition, and it is contained in the extremely narrow spectral bandwidth amounting to 1.7 nm at 8K and to 18 nm at room temperature. The phosphor under study can be efficiently excited making use of intense f-d transitions of Tb3+ in the UV-vacuum-UV region and may be of interest for applications requiring high spectral purity of the emission.