解决过程：
1、编辑/etc/my.cnf
在[mysqld] 配置部分添加一行
skip-grant-tables
 
2、保存后重启mysql
[root@localhost etc]# service mysqld restart
Shutting down MySQL.                                       [  OK  ]
Starting MySQL.                                                   [  OK  ]

3、登录数据库重新设置root密码

[root@localhost ~]# mysql -uroot -p mysql
Enter password:
直接回车进入

Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 1
Server version: 5.1.47-log Source distribution

Copyright (c) 2000, 2010, Oracle and/or its affiliates. All rights reserved.
This software comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to modify and redistribute it under the GPL v2 license

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
| mysql              |
| test               |
+--------------------+
3 rows in set (0.00 sec)

执行下列语句

mysql> update user set password=password("mysql") 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 (0.00 sec)
 
4、删除/etc/my.cnf文件中添加的“skip-grant-tables”行，重启mysql；
用新设的密码就能正常登录了；