Step # 1: Stop the MySQL server process.

  # /etc/init.d/mysql stop

Step # 2: Start the MySQL (mysqld) server/daemon process with the --skip-grant-tables option so that it will not prompt for a password.

# mysqld_safe --skip-grant-tables &

Step # 3: Connect to the MySQL server as the root user.

# mysql -u root

Step # 4: Set a new root password.

mysql> use mysql;
  mysql> update user set password=PASSWORD("NEW-ROOT-PASSWORD") where User='root';
  mysql> flush privileges;
  mysql> quit

Step # 5: Exit and restart the MySQL server.

# /etc/init.d/mysql stop