  Pulsars, especially millisecond pulsars, are intrinsically very stable
celestial clocks, and their great pulse period stability open up a wide range
of potential applications to astronomical phenomena, such as a natural detector
for very low frequency ($10^{-7}-10^{-9}$ Hz) gravitational waves (GWs)
background from supermassive black hole binaries. Double neutron star (DNS)
binary systems, containing one or two radio pulsars, lose orbital energy by
gravitational radiation, which leads to the orbital shrink. As a result, two
neutron stars get closer and closer, during which it contributes to the
emission of high frequency GWs of $1-10^4$ Hz. In this paper, we investigate
the frequency shift of pulse signal for radio pulsars in DNS system that is
induced by the emission of GWs from the system. We point out that the pulse
frequency shift of radio signal in these systems can be a potential tool to
hunt for the high-frequency GWs, with massive gravitons, from DNS systems,
which resorts to a temporal shift of gravitational constant $\delta G(t)/G$.
The sensitivity to high-frequency GWs from DNS by radio pulse frequency shift
is discussed. The correlation between timing residuals of pulsar pair in double
radio pulsars, such as the system PSR 0737-3039 A(B), is also considered.
