Seems like the accepted answer does not work anymore. I found the correct method from another post: https://stackoverflow.com/a/46811403/6368026
Now you should use:
http://www.youtube.com/embed/videoseries?list=USERID And the USERID is your youtube user id with 'UU' appended.
For example, if your user id is TlQ5niAIDsLdEHpQKQsupg then you should put UUTlQ5niAIDsLdEHpQKQsupg. If you only have the channel id (which you can find in your channel URL) then just replace the first two characters (UC) with UU.
So in the end you would have an URL like this:
http://www.youtube.com/embed/videoseries?list=UUTlQ5niAIDsLdEHpQKQsupg
I quickly did this for anyone else coming onto this page:
<object width="425" height="344">
<param name="movie" value="http://www.youtube.com/v/u1zgFlCw8Aw?fs=1"</param>
<param name="allowFullScreen" value="true"></param>
<param name="allowScriptAccess" value="always"></param>
<embed src="http://www.youtube.com/v/u1zgFlCw8Aw?fs=1"
type="application/x-shockwave-flash"
allowfullscreen="true"
allowscriptaccess="always"
width="425" height="344">
</embed>
</object>
In order to embed your channel, all you need to do is copy then paste the following code in another web-page.
<script src="http://www.gmodules.com/ig/ifr?url=http://www.google.com/ig/modules/youtube.xml&up_channel=YourChannelName&synd=open&w=320&h=390&title=&border=%23ffffff%7C3px%2C1px+solid+%23999999&output=js"></script>
Make sure to replace the YourChannelName with your actual channel name.
For example: if your channel name were CaliChick94066 your channel embed code would be:
<script src="http://www.gmodules.com/ig/ifr?url=http://www.google.com/ig/modules/youtube.xml&up_channel=CaliChick94066&synd=open&w=320&h=390&title=&border=%23ffffff%7C3px%2C1px+solid+%23999999&output=js"></script>
Please look at the following links:
You just have to name the URL to your channel name. Also you can play with the height and the border color and size. Hope it helps
Source: Stackoverflow.com