  In this paper we report the growth and superconductivity of $Na_xTaS_2$
crystals. The structural data deduced from X-ray diffraction pattern shows that
the sample has the same structure as $2H-TaS_2$. A series of crystals with
different superconducting transition temperatures ($T_c$) ranging from 2.5 K to
4.4 K were obtained. It is found that the $T_c$ rises with the increase of $Na$
content determined by Energy-Dispersive x-ray microanalysis(EDX) of Scanning
Electron Microscope (SEM) on these crystals. Compared with the resistivity
curve of un-intercalated sample $2H-TaS_2$ ($T_c$ = 0.8 K, $T_{CDW} \approx$ 70
K), no signal of charge density wave (CDW) was observed in samples
$Na_{0.1}TaS_2$ and $Na_{0.05}TaS_2$. However, in some samples with lower
$T_c$, the CDW appears again at about 65 K. Comparison between the anisotropic
resistivity indicates that the anisotropy becomes smaller in samples with more
$Na$ intercalation (albeit a weak semiconducting behavior along c-axis) and
thus higher $T_c$. It is thus concluded that there is a competition between the
superconductivity and the CDW. With the increase of sodium content, the rise of
$T_c$ in $Na_xTaS_2$ is caused mainly by the suppression to the CDW in
$2H-TaS_2$, and the conventional rigid band model for layered dichalcogenide
may be inadequate to explain the changes induced by the slight intercalation of
sodium in $2H-TaS_2$.
