How to migrate from WordPress 3.2.1 to Latest Version (As of now WP 3.6.1)

Some of the Plugins are not compatible for the newer version.

The same might be true for the site’s theme, so it would be best to check with its author before proceeding. After you have learned about that and have decided what to do there, if necessary, and after you have also decided what you will eventually do about incompatible plugins, be sure to do a database backup (typically via phpMyAdmin) and a backup of the wp-content folder and of the wp-config.php file before proceeding. At that point, disable all plugins at the Dashboard and then also momentarily rename the plugins folder to something like “plugins_hold” via FTP or SFTP to be certain all plugins actually are completely deactivated, then rename the plugins folder back to “plugins”. Next switch to a default WordPress theme, then try a WordPress update.
https://www.theistudio.com/muse/1519/wordpress-how-to-update-to-the-latest-wp-version

If all goes well, you should then be able to begin reactivating (one-at-a-time) whatever theme and plugins you know you can use with the latest version of WordPress. If the above does not work, I would next try a manual upgrade.
https://codex.www.ads-software.com/Updating_WordPress#Manual_Update
https://codex.www.ads-software.com/Upgrading_WordPress_Extended

I have completed the upgradation of wordpress successfully using the following steps.

Taken the site & db backup.

Dashboard ==> Updates

Upgrade the wordpress version of the website.

I haven’t deactivate any plugin.

Once the update process completed, Login to the admin panel.

As for as my situation, there is no issues with plugin.