As Ilja said, if you have a private method complex enough that you feel it needs testing, you would probably do yourself a favor by extracting some of those private methods into a new class and make them public over there.
If you feel that's overkill, the next best thing you could do is probably to test your private methods through your public methods--they're the ones making use of those private methods anyway, right?
Finally, if you really really really don't want to extract your private methods elsewhere and testing through the public methods is somehow cumbersome (which is even more evidence for the need to extract a class from those private methods!), yes, you can use the
Java Reflection API to invoke private methods from your test code. Google for PrivilegedAccessor or something like that.