  Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlations and
its intrinsic asymmetry makes it distinct from entanglement and Bell
nonlocality. We propose here a scheme for realizing one-way Gaussian steering
of two electromagnetic fields mediated by a mechanical oscillator. We reveal
that the steady-state one-way steering of the intracavity and output fields is
obtainable with different cavity losses or strong mechanical damping. The
conditions for achieving this asymmetric steering are found, and it shows that
the steering is robust against thermal mechanical fluctuations. The present
scheme can realize hybrid microwave-optical asymmetric steering by
optoelectromechanics. In addition, our results are generic and can also be
applied to other three-mode parametrically-coupled bosonic systems.
