Is it possible to add time line web-part using normal custom list or any other solution to implement through normal list
It's not part of the list, it's a separate webpart. On the page where you want the timeline insert a new web part, and under content rollup you will find the timeline.
** Edit **
You can't bind it to a "custom list" type. You can however create a task list and then extend it with the columns you need. This would let you use the timeline with that list.
You can't just add the task content type either - it has to start as a task list to work.