This is a solution for those who want to transfer contacts from iTunes backup to Android without iPhone.
Step 1: Install "iTunes to Android" Program
Install and run iTunes to Android on your computer.
Step 2: Choose a Transfer Mode
Click "From iTunes Backup" from the up-right sector.
Step 3: Select a Backup
Click the inverted triangle beside the box on the left column, then select the backup of your old iPhone.
Step 4: Connect Your New Android
Connect your new Android phone to computer via a USB cable. You will be asked to turn on USB debugging. Follow the instruction on the interface.
Step 5: Tick the File Type
Click on the icon of the file type that you want to transfer. Contacts, for example.
Step 6: Start to Transfer
Click "Start Copy" to transfer contacts from iTunes backup to Android.