MyISAM with Innodb in the same Wordpress database reduce performace? My new Wordpress database all the Wordpress created tables use InnoDB engine and plugin created table use MyISAM. But older site database all the tables use MyISAM table engine. 
I use MySQL 5.5.35-cll i686.

If I use two different table engines in a same database, it will reduce my site performance or are there any downside?
Having InnoDB won't make MyISAM slower and vice versa. However you have to be more careful in memory allocation for InnoDB and MyISAM. Because they store data and indexes in different buffers.
MyISAM:


Indexes in the key buffer
Data in file system cache


InnoDB:


Data and indexes (well, in InnoDB everything is indexes) in the buffer pool


So if you allocate more than necessary to InnoDB then MyISAM will have to access disk more often (and vice versa)