If you have never edited your YouTube channel URL and your URL looks something like this (http://www.youtube.com/channel/UCY3GS9HK953AaPiTRnTMTXw) then you might be able to change that URL by going into your Advanced Settings area and clicking on the Create Custom URL, as shows in the screenshot below:
To be eligible for a custom URL your account needs to meet these requirements:
- Be in good standing
- Have 100 subscribers or more
- Be at least 30 days old
- Have uploaded a photo as a channel icon
- Have uploaded a channel art
You can also qualify by linking and verifying your official webpage with your connected G+ Page.
Important: You can't change your custom URL after you create it.