Itunes asking me my billing verification again and again on the same computer. I don't know why it behave like this. Anyone can solve my problem?

Try the following steps,

Sign into your computer and removal of credit card information. Here are the steps:

1) Open iTunes and sign in to the iTunes Store.

2) Select "View My Account" from the Store menu.

3) Enter your password and click the View Account button.

4) Click the Edit Payment Information button.

5) Select "None" as the payment type.

6) Click the Done button at the bottom of the page.

Reset your account password from the following link:

http://iforgot.apple.com

Phase 3:

Download a free content on to get recognized in iTunes.

To ensure your account is functioning, try downloading a free item from the iTunes Store. To do this, navigate to the iTunes Store main page by clicking the Home icon near the upper-left corner of the window. Scroll down and click the "FREE ON iTunes" link near the bottom of the main page, then select an item to download.

After you are able to download the free App try updating the billing information as usual.

I have the same problem.

Trying to reach iTunes support.