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In this paper we report the growth and superconductivity of N axT aS2 crystals. The structural data deduced from X-ray diffraction pattern shows that the sample has the same structure as 2H − T aS2. A series of crystals with different superconducting transition temperatures (Tc) ranging from 2.5 K to 4.4 K were obtained. It is found that the Tc rises with the increase of N a 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 − T aS2 (Tc = 0.8 K, TCDW ≈ 70 K), no signal of charge density wave (CDW) was observed in samples N a0.1T aS2 and N a0.05T aS2. However, in some samples with lower Tc, the CDW appears again at about 65 K. Comparison between the anisotropic resistivity indicates that the anisotropy becomes smaller in samples with more N a intercalation (albeit a weak semiconducting behavior along c-axis) and thus higher Tc. It is thus concluded that there is a competition between the superconductivity and the CDW. With the increase of sodium content, the rise of Tc in N axT aS2 is caused mainly by the suppression to the CDW in 2H − T aS2, 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 − T aS2.