We have surveyed Andromeda VI, a dwarf spheroidal galaxy companion to M31, for variable stars by using F450W and F555W observations obtained with the Hubble Space Telescope on 1999 October 25 and 1999 October 27 (WFPC2 instrument). A total of 118 variables were found, including 111 RR Lyrae stars, six anomalous Cepheids, and one variable that we were unable to classify. We find that the Andromeda VI anomalous Cepheids have properties consistent with those of anomalous Cepheids in other dwarf spheroidal galaxies. We revise the existing period-luminosity relations for these variables. Further, using these and other available data, we show that there is no clear difference between fundamental and first-overtone anomalous Cepheids in a period-amplitude diagram at shorter periods, unlike the RR Lyrae stars. For the Andromeda VI RR Lyrae stars, we find that they lie close to the Oosterhoff type I Galactic globular clusters in the period-amplitude diagram, although the mean period of the RRab stars, <P_ab_>=0.588days, is slightly longer than that of the typical Oosterhoff type I cluster. The mean V magnitude of the RR Lyrae stars in Andromeda VI is 25.29+/-0.03, resulting in a distance 815+/-25kpc on the Lee, Demarque, & Zinn (1990ApJ...350..155L) distance scale. This is consistent with the distance derived from the I magnitude of the tip of the red giant branch. Similarly, the properties of the RR Lyrae stars indicate a mean abundance for Andromeda VI that is consistent with that derived from the mean red giant branch color.