  We reconstruct the dark energy density $\rho_X(z)$ as a free function from
current type Ia supernova (SN Ia) data (Tonry et al. 2003; Barris et al. 2003;
Knop et al. 2003), together with the Cosmic Microwave Background (CMB) shift
parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure
(LSS) growth factor from 2dF galaxy survey data. We parametrize $\rho_X(z)$ as
a continuous function, given by interpolating its amplitudes at equally spaced
$z$ values in the redshift range covered by SN Ia data, and a constant at
larger $z$ (where $\rho_X(z)$ is only weakly constrained by CMB data). We
assume a flat universe, and use the Markov Chain Monte Carlo (MCMC) technique
in our analysis. We find that the dark energy density $\rho_X(z)$ is constant
for $0 \la z \la 0.5$ and increases with redshift $z$ for $0.5 \la z \la 1$ at
68.3% confidence level, but is consistent with a constant at 95% confidence
level. For comparison, we also give constraints on a constant equation of state
for the dark energy.
  Flux-averaging of SN Ia data is required to yield cosmological parameter
constraints that are free of the bias induced by weak gravitational lensing
\citep{Wang00b}. We set up a consistent framework for flux-averaging analysis
of SN Ia data, based on \cite{Wang00b}. We find that flux-averaging of SN Ia
data leads to slightly lower $\Omega_m$ and smaller time-variation in
$\rho_X(z)$. This suggests that a significant increase in the number of SNe Ia
from deep SN surveys on a dedicated telescope \citep{Wang00a} is needed to
place a robust constraint on the time-dependence of the dark energy density.
