One account with multiple contacts, when importing, only one contact was imported

I imported a csv file into CRM 2011 with automatic duplicate detection. the csv file contains both account and contact information. So whenever I imported, both records are imported together. After completing the import, no account is duplicated, but only one contact is imported if there are more contacts in one account. I repeated the import, it showed those contacts whose accounts are already in the system still cannot be imported.

The error message is "A record was not created or updated because a duplicate of the current record already exists."

I'm thinking if I can just import contacts from the same source file without importing accounts, and how to do?

or are there any other ways I can do to solve this problem?

thanks, Clare