How to Change iTunes Password on iPhone
The account password located in the iTunes Store application on your iPhone is used to make media purchases through the iTunes and App Store, and can be changed through your iPhone. Similar to the iTunes program on your computer, the iTunes Store app displays your account information and allows you to change your email address, password and payment method. Once changed, the new password will be automatically updated on all devices that use your iTunes account.
Push the "Home" button on your iPhone, and slide the onscreen bar to unlock the device.
Tap the "iTunes" icon on the home screen, and tap the "Music" icon at the bottom of the application screen.
Slide your finger up against the screen to scroll down, and tap the "Account" tab at the bottom of the screen.
Tap "View Account," and tap the "Continue" button in the pop-up box.
Enter your current iTunes account password, and tap the "OK" button to sign in.
Tap the "Apple ID" tab under the "Edit Account Info" section, and tap the "Password" field.
Tap the backspace button above the "Go" button in the lower-right corner of the screen, and enter the new password in both the "Password" and "Verify" field. Tap the "Go" button to save the new password.