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FRW universe in Horava-Lifshitz (HL) gravity model filled with a combinationof dark matter and dark energy in the form of variable modified Chaplygin gas(VMCG) is considered. The permitted values of the VMCG parameters aredetermined by the recent astrophysical and cosmological observational data.Here we present the Hubble parameter in terms of the observable parameters$\Omega_{dm0}$, $\Omega_{vmcg0}$, $H_{0}$, redshift $z$ and other parameterslike $\alpha$, $A$, $\gamma$ and $n$. From Stern data set (12 points), we haveobtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$test. The best-fit values of the parameters are obtained by 66\%, 90\% and 99\%confidence levels. Next due to joint analysis with BAO and CMB observations, wehave also obtained the bounds of the parameters ($A,\gamma$) by fixing someother parameters $\alpha$ and $n$. The best fit value of distance modulus$\mu(z)$ is obtained for the VMCG model in HL gravity, and it is concluded thatour model is perfectly consistent with the union2 sample data.

Observational data fitting to constrain Variable Modified Chaplygin Gas in the background of Horava-Lifshitz Gravity