Stop Mysql.
Start Mysql with below command
mysqld_safe --skip-grant-tables &
Loggin into mysql terminal
mysql --user=root mysql
Press enter if asked for password
Update the password
update user set Password=PASSWORD('new_Password') WHERE User='root';
Exit from mysql terminal
Kill the process started by you
Start mysql through init script and login through your new password.
/etc/init.d/mysql start
mysql --user=root mysql -p
