  We study the generation of a stochastic gravitational wave (GW) background
produced by a population of neutron stars (NSs) which go over a hadron-quark
phase transition in its inner shells. We obtain, for example, that the NS phase
transition, in cold dark matter scenarios, could generate a stochastic GW
background with a maximum amplitude of $h_{\rm BG} \sim 10^{-24}$, in the
frequency band $\simeq 20-2000 {\rm Hz}$ for stars forming at redshifts of up
to $z\simeq 20.$ We study the possibility of detection of this isotropic GW
background by correlating signals of a pair of `advanced' LIGO observatories.
