In this paper, inspired by the investigations on the theory of cosmological
perturbations in Ho\v{r}ava-Liftshit cosmology, we calculated the spectrum of
primordial perturbation leaded by a scalar field with modified dispersion
relation \omega\sim k^z/a^{p-1}, in which z is the critical exponent and p is
generally not equal to z. We discussed that for fixed z, if the spectrum is
required to be scale invariant, how should p depend on the background
evolution. We concluded that there is always a room of parameters for the
generation of scale invariant spectrum.Comment: 8 pages, 2 figure