Below
is a tutorial on how to transfer contacts from Android to iPhone in a simple way, with the help of Android File Transfer. Preparation:
Download and Install Android File
Transfer to your computer. (Free Trial version available at the bottom link)
Pre-install
iTunes on your computer, because certain services of iTunes are required to
access iPhone data.

Note: If you want to recover deleted data from Android mobile, you can use Android Recovery app.
Step 1: Launch the program and enter transfer mode
Start
Android File Transfer, and click “Phone to Phone Transfer” to get ready
for transfer.
Step 2: Connect both your phones to computer
Using
two USB cables, connect your phones to computer. If well connected, both models
should be shown on the interface as below.
Transfer
process will be from “Source” to “Destination”
Step 3: Transfer contacts from Android to iPhone
If
you want to transfer contacts from Android to iPhone, your Android model should
be on the left “Source” side. Click "Flip" can change position. Select
“Contacts” in the middle, and
uncheck other contents. Confirm the options and click “Start Copy”. When it’s over, click “OK” to finish.
Note:
Mark “Clear data before copy” only
if you want to remove the destination phone’ contacts before copy. It will remove
corresponding data you select in the middle.
Now
you should have your contacts copied to the other phone. If you feel like to
have a try or practice, download the Free Trial version and see.

Android File Transfer can works between iOS,
Android, Symbian, with backup and recovery function too. For example:
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