Small problem.

You have two YouTube histories that you need to clear. The history of your searches for videos, and the history of videos that you watched.

This should tell you how to do it:
http://support.google.com/youtube/answer/95725?hl=en

If it is unclear, google something like "clear youtube history" and you should find endless tutorials. It's how I found the link I just gave you. I picked this one because it appears to me to come from an official source. (Google runs YouTube I think.)


EDIT: Although I notice that you mention a website for downloading from YouTube, not YouTube itself. If you are worried about a history on a third-party download website, you'll probably need to check their help page or something. Or perhaps google "clear XXXX history" with XXXX being the name of whatever website you are concerned about.

I couldn't give a more specific answer about a third-party download website without knowing the name of website.

I didn't signed in the youtube video downloading website,so no history arises.Can you answer the question once more by reading the question.

Yes, you do are guilty.

Signing in may not be necessary. You could be tracked by cookies for example.

I re-read your question. I am not sure what more I can add.

How,I didn't uploaded the video from phone or uploaded the video from url,I just did a bad search and downloaded the video.but that youtube video downloading website may be showed that video in the recent downloads that contain other videos downloaded by others(users).It was replaced by other video because of lot of other downloads of others.

The video that I downloaded may be showed in the recent downloads that contain other users downloaded video until it was replaced by others recent downloads.What is your thought on it.

It's possible. But if it isn't connected to you in any way, and if it has long since been displaced by more recent downloads, then it shouldn't be anything to worry about.

Thanks.