Hi Kanmani,
One way is to loop over each Group (see reference 1) and retrieve user's blog posts (see reference 2) from that group.
References:
1. Looping over all Groups: http://docs.liferay.com/portal/6.1/javadocs/com/liferay/portal/service/GroupLocalServiceUtil.html#getCompanyGroups(long, int, int)
2. Getting all Blog posts by user for a particular group: http://docs.liferay.com/portal/6.1/javadocs/com/liferay/portlet/blogs/service/BlogsEntryLocalServiceUtil.html#getGroupUserEntries(long, long, java.util.Date, int, int, int, com.liferay.portal.kernel.util.OrderByComparator)
Let me know if you have question.
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Firmi prego dentro per inbandierare questo come inadeguato.