According to this help page for the CallerID Blocker app, blocking your number (i.e. your Caller ID) is not available with any network in Vietnam.

You can try a few things, but at the end of the day it may be impossible. It's not your phone that does the actual blocking, but your service provider, so ultimately anything could happen.

Dual SIM

If you want to keep people from finding out your actual number, you could consider getting a second SIM card for the times you don't want to provide your actual number. A Dual SIM cellphone would make this especially easy, allowing you to select which number to use for each call.

Phone Setting

If you really want to use just one SIM, first know that the phone setting for blocking Caller ID is not just available on iPhone. It's also on Android, Windows Phone 8, Blackberry, and presumably more. It might be worth checking your phone manual or googling something like "[Phone model] block Caller ID" if you do not have one of these phones. According to Lifehacker Australia:

On iPhones, it's found under Settings>Phone>Show My Caller ID

On Android devices it should be found by going into the menu from the phone dialler, choosing additional settings and then caller ID

On Windows Phone 8 devices, go to the dialler, choose the ellipses, then settings, then "Show My Caller ID"

On Blackberry devices, swipe down in the phone dialler and choose the cog icon. The default option is "Show my number". Tapping on that should bring up "Allow My Number to Appear" which you can then switch to off.

There is no guarantee this will setting will work, however, as your service provider is the one that actually blocks your Caller ID. The built-in phone setting is just a convenient way to communicate your intent to your provider.

Other

If that doesn't work, my only other suggestion is to contact your phone provider in Vietnam, or try searching for a list of self-service codes for your provider and hope it includes one to block your number (like this list).