I do plan on designing the web browser with visual basic, but if I distribute it, only people with Windows PC's can use it.
You do realise that .Net (and hence VB) is strictly speaking only for Windows? You can use Mono to run .Net applications on some other platforms but it is not 100% compatible with all aspects of the .Net framework.

If you truly want cross-platform compatibility you may be better off writing it in Java or some other language.