Check for valid link (URL)

The following works in Bash >= version 3.2 without using grep:

regex='(https?|ftp|file)://[-[:alnum:]\+&@#/%?=~_|!:,.;]*[-[:alnum:]\+&@#/%=~_|]'
string='http://www.google.com/test/link.php'
if [[ $string =~ $regex ]]
then 
    echo "Link valid"
else
    echo "Link not valid"
fi

I simplified your regex by using [:alnum:] which also matches any alphanumeric character (e.g. Э or ß), but support varies by the underlying regex library. This is another potential simplification which uses + instead of * and a repeated sequence (although your second sequence is different from the first).

regex='(https?|ftp|file)://[-[:alnum:]\+&@#/%?=~_|!:,.;]+'

Since I don't have enough rep to comment above, I am going to amend the answer given by Dennis above with this one.

I incorporated Christopher's update to the regex and then added more to it so that the URL has to at least be in this format:

http://w.w (has to have a period in it).

And tweaked output a bit :)

regex='^(https?|ftp|file)://[-A-Za-z0-9\+&@#/%?=~_|!:,.;]*[-A-Za-z0-9\+&@#/%=~_|]\.[-A-Za-z0-9\+&@#/%?=~_|!:,.;]*[-A-Za-z0-9\+&@#/%=~_|]$'

url='http://www.google.com/test/link.php'
if [[ $url =~ $regex ]]
then 
    echo "$url IS valid"
else
    echo "$url IS NOT valid"
fi

Probably because the regular expression is written in PCRE syntax. See if you have (or can install) the program pcregrep on your system - it has the same syntax as grep but accepts Perl-compatible regexes - and you should be able to make that work.

Another option is to try the -P option to grep, but the man page says that's "highly experimental" so it may or may not actually work.

I will say that you should think carefully about whether it's really appropriate to be using this or any regex to validate a URL. If you want to have a correct validation, you'd probably be better off finding or writing a small script in, say, Perl, to use the URL validation facilities of the language.

EDIT: In response to your edit in the question, I didn't notice that that regex is also valid in "extended" syntax. I don't think you can get better/faster than that.