I want to monitor private message and want to check and store at admin side. so admin can see who doing message to whom and make the policy for to sending the message.
You need to enable the
Manage Chatter Messages system permission on a cloned System Administrator profile before you have access to these sObjects.
ChatterConversation objects is what you are looking for.
SELECT Body,ConversationId,Id,SenderId,SentDate FROM ChatterMessage
To be honest, if you do this you should make all your users aware of this, and I'm not sure if this might be affected by local regulations. Here, system admins are for instance not allowed by law to check employee mails on the mailserver for instance. (As far as I'm informed).
Sometimes, to get your users at their top efficiency, the best way is to give them the freedom and let go of some control/monitoring.