  In this paper we consider an inflating universe with long straight cosmic
string along z-axis. We show that the effect of cosmic string can be taken as a
perturbation on the background of FRW metric. Then by doing cosmological
perturbations on this inflating cosmic string background, we find linearized
Einstein field equations. We show that at leading order (ignoring the mixing
terms of cosmic string perturbations with gravitational tensor perturbations),
the cosmic string appears as an inhomogeneous term on the right hand side of
wave equation of tensor perturbations . Then by finding analytical solution of
the wave equation for slow-roll inflation, we show how it effects on the
spectrum of primordial gravitational waves.
