I am using google analytics to track my website results.
But in traffic source referring site it shows that visitors comes from my site itself.
i.e. my site is xyz.com in the referring site it show visitors are coming from xyz.com
Do you think you have traffic from search engines too but you don't see it in Google analytics? If you think Google analytics doesn't give you right results, you can use Awstats or any other such program. But i myself think Google analytics gives true statistics.