In iTunes click your device at the side then info at the top and make sure sync contacts is ticked.
Besides i share you a article about how to transfer contacts from iPhone to computer, which can help you backup all iPhone contacts and contact photos from iPhone to your computer and keep them safe on the computer.
Cheers.
More reviews:
http://www.levesoft.com/how-to-transfer-and-backup-contacts-from-iPhone-to-pc.html
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I backed up and synced on iTunes and all my iPhone contacts were lost
Fulqure says,
When I synced on iTunes all my contacts were lost. Favorites became just numbers with no names. What happened? If any way to transfer my iPhone contacts to computer without itunes?
Thanks in advance.