  By the use of homotopy perturbation method-Pad\'e (HPM-Pad\'e) technique, a
new analytical approximation of luminosity distance in the flat universe is
proposed, which has the advantage of significant improvement for accuracy in
approximating luminosity distance over cosmological redshift range within
$0\leq z\leq 2.5$. Then we confront the analytical expression of luminosity
distance that is obtained by our new approach with the observational data, for
the purpose of checking whether it works well. In order to probe the robustness
of the proposed method, we also confront it to supernova type Ia and recent
data on the Hubble expansion rate $H(z)$. Markov Chain Monte Carlo (MCMC) code
emcee is used in the data fitting. The result indicates that it works fairly
well.
