Hello Yamoo
I have recently upgraded a Netbackup Server environment from version 6.5.5 to 7.1. You can directly upgrade the version 6.x to 7.1. What my recommandation is
1.) First you should take the backup of Catalog and also keep the DR file some where on the Network.
2.) Download the 7.1 patch which may be frustrating sometime. I have a post which may decrease your tension in downloading the 7.1 product. See the below link for your reference:
https://www-secure.symantec.com/connect/forums/not-able-find-version-7-netbackup
One things which is important in this post
Call Symantec Sales for the notification ID which you put in the https://licensing.symantec.com to download the 7.1 product OR they will give you the serial no which you put in the fileconnect Site to download the product 7.1.
Note:
If you also have DLO for Netbackup installed on the machine on which Netbackup Server is installed (in my case i have DLO installed and i also upgraded win2003 to win2008) and you are also planning to upgrade the OS with the Netbackup ,So you will face problem because win2008 OS will only support DLO 6.1 with MP6. See the below post for your reference.
https://www-secure.symantec.com/connect/forums/how-install-dlo-win2008