I have migrated a site from SP 2010 to SP 2013, It contains custom master page. It has been developed based on v4.masterpage. After Migrating the master Page looks like the below screen shot. Please guide me how to solve this error
No easy answer. Seems like the styling is off for a number of elements on the page.
The most easy way out is as Amal describes and start pretty much all over. You can start with the master pages found here
And checking out "Starter foundation" would be appropriate in your case as it seems it might be a standard team site.
I think you have already run the visual upgrade on your site collection. If not, I would try it. Although I have been through times when visual upgrade ruins more elements than fixes.
My preferred solution would be to change the master page to Seattle or Oslo, which would at least fix the UI for time being. And then go back to the question, do I need to invest my development time into creating a new master page? If yes, go ahead with design manager.