Connect your old iPhone to your computer and open iTunes.Click on your iPhone in the Devices section, and then click "Info."
Click the "Sync Contacts" option, and then select "All Contacts"
Click the "Apply" button, wait for the sync to complete, and then press the "Eject" button to disconnect your old iPhone from the computer.
Attach your new iPhone and select it from the Devices section. Click the "Info" tab, and then tick the "Sync Contacts" check box.
Apply the same settings you applied to your old iPhone: choose the "All Contacts" sync options, click the "Apply" button to transfer your contacts to your new iPhone.