Create new mysql user with grant option

Login in mysql using:

$ mysql -u root -p

First create a database using:

mysql> create database dbname;
Query OK, 1 row affected (0.00 sec)

Then in mysql shell create new user using:

mysql> create user 'username'@'localhost' IDENTiFIED BY 'password';
Query OK, 0 rows affected (0.00 sec)

mysql> grant all privileges on dbname.* to 'username'@'localhost' with grant option;
Query OK, 0 rows affected (0.00 sec)

Or you can use ‘%’ wildcard if you want to connect mysql from any host:

mysql> create user 'username'@'%' IDENTiFIED BY 'password';
Query OK, 0 rows affected (0.00 sec)

mysql> grant all privileges on dbname.* to 'username'@'%' with grant option;
Query OK, 0 rows affected (0.00 sec)

For more details visit mysql manual.