  Approximate vacuum solutions of Jordan-Brans-Dicke theory for perturbed
scalar field and perturbed Robertson-Walker metric, are found. Solutions for
the scale factor and the scalar field in unperturbed JBD theory are dependent
on the $\omega$ parameter which determines how the scalar field is coupled to
geometry of space-time. After adding a metric perturbation to Robertson-Walker
metric and a perturbation to the scalar field, we solved the linearized JBD
equations and found the scale factor and the scalar field as $a\propto t$ and
$\phi\propto t^{-2}$ with $\omega=$-3/2. The results are necessary conditions
for ordinary and scalar gravitational waves to exist in the vacuum case.
Despite omega is a large positive number for current solar system environment
observations, this value of omega makes JBD theory conformally invariant and
fits recent supernovae type Ia data. We also looked for the value of omega for
the case which has nonzero spatial curvature parameter.
