Whenever I added new contacts to my iPhone, on the next sync, iTunes would ask me if I wanted to copy them to my Mac as well. Photos and music can't easily be synced from phone to Mac, but contacts can.
Ah, here it is. I just found it with my iPhone. Plug the iPhone into the computer. When iTunes starts up, click on the iPhone in the panel on the left-hand side. You'll see a screen that has a lot of options along the top: "Summary," "Info," "Apps," "Tones," "Music," and so on.
Click Info. In the top of the Info pane, turn on the option "Sync Address Book Contacts."
What's more, you can refer this tutorial about how to transfer iPhone contacts to my Mac computer.
iphone-mac.com/how-to-transfer-contacts-from-iphone-to-mac.html
Hope it helps.
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