To change MySQL's root user password:

Step 1: Stop the MySQL server.

• in Ubuntu or Debian:
  sudo /etc/init.d/mysql stop
• in CentOS, Fedora or Red Hat Enterprise Linux:
  sudo /etc/init.d/mysqld stop

Step 2: Start the MySQL server without the privilege system.

sudo mysqld_safe --skip-grant-tables &

or, if mysqld_safe is unavailable,

sudo mysqld --skip-grant-tables &

Step 3: Connect to the MySQL server.

mysql -u root

Step 4: Set a new password for root user.

FLUSH PRIVILEGES;
ALTER USER 'root'@'localhost' IDENTIFIED BY 'new_password';
FLUSH PRIVILEGES;
exit;

FLUSH PRIVILEGES;
SET PASSWORD FOR 'root'@'localhost' = PASSWORD('new_password');
FLUSH PRIVILEGES;
exit;

Note: The ALTER USER syntax was introduced in MySQL 5.7.6.

Step 5: Restart the MySQL server.

• in Ubuntu or Debian:
  sudo /etc/init.d/mysql stop
sudo /etc/init.d/mysql start
• in CentOS, Fedora or Red Hat Enterprise Linux:
  sudo /etc/init.d/mysqld stop
sudo /etc/init.d/mysqld start

When we want to change root password in windows, We need to follow following steps :

Step 1 : Start your Command Prompt by using any of below method :

Perss Crtl+R or Goto Start Menu > Run and then type cmd and hit enter

Step 2 : Change your directory to where MYSQL is installed, In my case it's

C:\> cd C:\mysql\bin

Step 3 : Now we need to start mysql command prompt

C:\mysql\bin> mysql -u root mysql

Step 4 : Fire query to change root password

mysql> SET PASSWORD FOR root@localhost=PASSWORD('my_new_password');

1. Stop the MySQL (mysqld) server/daemon process.
2. Start the MySQL server process the --skip-grant-tables option so that it will not prompt for a password: mysqld_safe --skip-grant-tables &
3. Connect to the MySQL server as the root user: mysql -u root
4. Change password:

• (5.7.6 and newer): ALTER USER 'root'@'localhost' IDENTIFIED BY 'new-password';
• (5.7.5 and older, or MariaDB): SET PASSWORD FOR 'root'@'localhost' = PASSWORD('new-password); flush privileges; quit;

5. Restart the MySQL server.

Note: this will work only if you are physically on the same server.

Online Doc: http://dev.mysql.com/doc/refman/5.7/en/resetting-permissions.html