Method 1:
在/usr/local/mysql/bin/下：
./mysqladmin -u root password new_password
一般安装时用此方法设置。

Method 2:
在mysql状态下：
mysql>UPDATE user SET password=PASSWORD(new_password) WHERE user=root;
mysql>FLUSH PRIVILEGES;

Method 3:
mysql>SET PASSWORD FOR root=PASSWORD(new_password);

有人会问如果不知道mysql root的密码情况下，是否可以修改密码呢？答案：可以的，想知道方法请继续往下看：

只有在mysqld启动的时候加上 --skip-grant-tables就ok，

例：

[root@server]# /usr/local/mysql/bin/mysqld_safe --skip-grant-tables &

[root@server]# /usr/local/mysql/bin/mysql -uroot -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or g.
Your MySQL connection id is 7
Server version: 5.0.45-log Source distribution

Type help; or h for help. Type c to clear the buffer.

mysql> use mysql;
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> update user set password=password(******)where user=root;
Query OK, 4 rows affected (0.00 sec)
Rows matched: 4 Changed: 4 Warnings: 0

mysql> flush privileges;
Query OK, 0 rows affected (0.01 sec)

杀掉mysql的进程或者重新启动mysql，然后重新登录，密码生效。