determined by SNe Ia observations is $$\chi_{\rm SN}^2=\sum_{i=1}^{157}{[\mu_{\rm obs}(z_i)-\mu_{\rm
th}(z_i)]^2\over \sigma_i^2}~,\label{chisn}$$ where the extinction-corrected distance moduli $\mu(z)$ is defined as $\mu(z)=m(z)-M$, and $\sigma_i$ is the total uncertainty in the observation. Following the Ref. [@IXCDM], we fix $\Omega_b^0=0.05$ in the computation for simplification. Hence, the computation is carried out in a four-dimensional space, for the four parameters $P=(\eta, w_X, h,
\Omega_{dm}^0)$. For the CMB, we use only the measurement of the CMB shift parameter [@cmbshift], $${\cal R}=\sqrt{\Omega_m^0}\int_0^{z_{\rm dec}}{dz\over
E(z)}~,\label{R}$$ where $\Omega_m^0=\Omega_{dm}^0+\Omega_b^0$, and $z_{\rm dec}=1089$ [@wmap]. Note that this quantity is irrelevant to the parameter $H_0$ such that provides robust constraint on the dark energy model. The results from CMB data correspond to ${\cal R}_0=1.716\pm 0.062$ (given by WMAP, CBI, ACBAR) [@wmap; @cbi]. We include the CMB data in our analysis by adding $\chi_{\rm CMB}^2=[({\cal R}-{\cal R}_0)/\sigma_{\cal
R}]^2$ (see e.g. Refs. [@wangyun; @Xia; @starob]), where ${\cal
R}$ is computed by the NGCG model using equation (\[R\]). The only large scale structure information we use is the parameter $A$ measured by SDSS [@sdssred], defined by $$A=\sqrt{\Omega_m^0}E(z_1)^{-1/3}\left[{1\over
z_1}\int_0^{z_1}{dz\over E(z)}\right]^{2/3}~,\label{A}$$ where $z_1=0.35$. Also, we find that this quantity is independent of $H_0$ either, thus can provide another robust constraint on the model. The SDSS gives 