  Based on our previous work on the differential geometry for the closed string
double field theory, we construct a Yang-Mills action which is covariant under
O(D,D) T-duality rotation and invariant under three-types of gauge
transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge
symmetries. In double field formulation, in a manifestly covariant manner our
action couples a single O(D,D) vector potential to the closed string double
field theory. In terms of undoubled component fields, it couples a usual
Yang-Mills gauge field to an additional one-form field and also to the closed
string background fields which consist of a dilaton, graviton and a two-form
gauge field. Our resulting action resembles a twisted Yang-Mills action.
