can't connect to mysql database locally but can connect to remotely

Dear esteem experts:

I got a funny situation here for my Mysql database server. I can connect to this database from a remote server but can't through local terminal.

here is the output I got:

[root@hera ~]# mysql -u root -h localhost -p
Enter password:
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)
[root@hera ~]#

---------------------------------------------------
but I can connect through a windows server:

C:\Program Files\MySQL\MySQL Server 5.5\bin>mysql -u root -p -h hera.minkagroup.
net
Enter password: ********
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 8871
Server version: 5.1.61 Source distribution

Copyright (c) 2000, 2012, Oracle and/or its affiliates. All rights reserved.

Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

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

mysql>



--------------------------------------
I guess my predecessor set up some permission limit like only permit "root" user to connect from a specific machine. Would you guys help me trouble shoot this.

thank you.