  Based on the data release of the Large Sky Area Multi-Object Fiber
Spectroscopic Telescope survey (LAMOST DR5) and the \emph{Gaia} Early Data
Release 3 (\emph{Gaia} EDR3), we construct a sample containing 46,109 giant
(log~$\emph{g}$ $\leqslant$ 3.5\,dex) stars with heliocentric distance d
$\leqslant$ 4 kpc, and the sample is further divided into two groups of the
inner ({\RGC} $<$ 8.34 \,kpc) and outer region ({\RGC} $>$ 8.34\,kpc). The
{\LZ} distributions of our program stars in the panels with different [Fe/H]
and [$\alpha$/Fe] suggest that the thick-disk consists of two distinct
components with different chemical compositions and kinematic properties. For
the inner region, the metal-weak thick disk (MWTD) contributes significantly
when [$\alpha$/Fe] $>+$0.2\,dex and [Fe/H] $<-$0.8\,dex, while the canonical
thick-disk (TD) dominates when [Fe/H]$>-$0.8\,dex. However, MWTD clearly
appears only when [$\alpha$/Fe] $>+$0.2\,dex and [Fe/H] $<-$1.2\,dex for the
outer region, and its proportion is lower than that of the inner region within
the same metallicity. Similar result can be obtained from the {\VP}
distribution. The high fraction of MWTD in the inner than that in the outer
region imply that MWTD may form in the inner disk, and is an observational
evidence about the inside-out disk formation scenario.
