  We construct a new X-ray (2--10 keV) luminosity function of Compton-thin
active galactic nuclei (AGNs) in the local universe, using the first MAXI/GSC
source catalog surveyed in the 4--10 keV band. The sample consists of 37
non-blazar AGNs at $z=0.002-0.2$, whose identification is highly ($>97%$)
complete. We confirm the trend that the fraction of absorbed AGNs with $N_{\rm
H} > 10^{22}$ cm$^{-2}$ rapidly decreases against luminosity ($L_{\rm X}$),
from 0.73$\pm$0.25 at $L_{\rm X} = 10^{42-43.5}$ erg s$^{-1}$ to 0.12$\pm0.09$
at $L_{\rm X} = 10^{43.5-45.5}$ erg s$^{-1}$. The obtained luminosity function
is well fitted with a smoothly connected double power-law model whose indices
are $\gamma_1 = 0.84$ (fixed) and $\gamma_2 = 2.0\pm0.2$ below and above the
break luminosity, $L_{*} = 10^{43.3\pm0.4}$ ergs s$^{-1}$, respectively. While
the result of the MAXI/GSC agrees well with that of HEAO-1 at $L_{\rm X} \gtsim
10^{43.5}$ erg s$^{-1}$, it gives a larger number density at the lower
luminosity range. Comparison between our luminosity function in the 2--10 keV
band and that in the 14--195 keV band obtained from the Swift/BAT survey
indicates that the averaged broad band spectra in the 2--200 keV band should
depend on luminosity, approximated by $\Gamma\sim1.7$ for $L_{\rm X} \ltsim
10^{44}$ erg s$^{-1}$ while $\Gamma\sim 2.0$ for $L_{\rm X} \gtsim 10^{44}$ erg
s$^{-1}$. This trend is confirmed by the correlation between the luminosities
in the 2--10 keV and 14--195 keV bands in our sample. We argue that there is no
contradiction in the luminosity functions between above and below 10 keV once
this effect is taken into account.
