  We have considered the FRW universe in loop quantum cosmology (LQC) model
filled with the dark matter (perfect fluid with negligible pressure) and the
modified Chaplygin gas (MCG) type dark energy. We present the Hubble parameter
in terms of the observable parameters $\Omega_{m0}$, $\Omega_{x0}$ and $H_{0}$
with the redshift $z$ and the other parameters like $A$, $B$, $C$ and $\alpha$.
From Stern data set (12 points), we have obtained 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, we have also obtained the bounds
of the parameters ($B,C$) by fixing some other parameters $\alpha$ and $A$.
From the best fit of distance modulus $\mu(z)$ for our theoretical MCG model in
LQC, we concluded that our model is in agreement with the union2 sample data.
