We report the observation of W-annihilation decay Ds+→ωπ+ and evidence for Ds+→ωK+ in a data sample corresponding to an integrated luminosity of 3.19 fb-1 collected with the BESIII detector at a center-of-mass energy s=4.178 GeV. We obtain the branching fractions B(Ds+→ωπ+)=(1.77±0.32stat±0.13sys)×10-3 with a significance of 6.7σ and B(Ds+→ωK+)=(0.87±0.24stat±0.08sys)×10-3 with a significance of 4.4σ. This measurement provides critical information to determine the nonperturbative W-annihilation amplitudes and shows the potential of searching for CP asymmetry in Ds+→ωK+. © 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.