  We study a string motion in the Lunin-Maldacena background, that is, the
\beta-deformed AdS_5 \times \tilde{S}^5 background dual to a \beta-deformation
of \mathcal{N} = 4 super Yang-Mills theory. For real \beta we construct a
rotating and wound string solution which has two unequal spins in \tilde{S}^5.
The string energy is expressed in terms of the spins, the winding numbers and
the deformation parameter. In the expansion of \lambda/J^2 with the total spin
J and the string tension \sqrt{\lambda} we present ``one-loop" and ``two-loop"
energy corrections. The ``one-loop" one agrees with the one-loop anomalous
dimension of the corresponding gauge-theory scalar operators obtained in
hep-th/0503192 from the \beta-deformed Bethe equation as well as the
anisotropic Landau-Lifshitz equation.
