  Cosmological observations indicate that our universe is flat and dark energy
(DE) dominated at present. The luminosity distance plays an important role in
the investigation of the evolution and structure of the universe. Nevertheless,
the evaluation of the luminosity distance d_L is associated computationally
heavy numerical quadratures in practice. In this Letter we find a series
solution of the luminosity distance in a spatially flat LCDM cosmological
model. And it is further shown that the series solution has a relative error of
less than 0.36% for any relative parameter \beta (\beta = Omega_m / Omega_L)
from zero to four, i.e. 0.2 < Omega_L < 1 and redshift z > 0.1 when the order
of the series is n = 100.
