//descriptors[@type="CTC"]/descriptor/mainterm
[download]

Using XML::LibXML, the syntax is something like

for my $mainterm (
    $doc->findnodes( '//descriptors[@type="CTC"]/descriptor/mainterm' 
+)
) {
    print $mainterm->toString();
}
[download]

XML::Twig would also be awesome here.

Update: Changed
//descriptors[type="CTC"]/mainterm
to
//descriptors[@type="CTC"]/descriptor/mainterm
as per reply.

I got better results with

$doc->findnodes( '//descriptors[@type="CTC"]/descriptor/mainterm/text(
+)'
[download]

The three changes I added are:
• an @ for the type attribute
• the /descriptor element (although the xml is not well formed)
• /text() since it appears they desire a text node

arg, yeah, dumb mistakes. But not the third one. Contrary to your claims, the OP wants the whole element ('<mainterm weight="a">G</mainterm>'), not just the text ('G').

use strict;
use warnings;
use XML::Twig;

my $xfile = shift;
my $t = new XML::Twig(
   twig_handlers => {descriptors => \&desc}
);
$t->parsefile($xfile);

sub desc {
    my ($twig, $desc) = @_;
    if ($desc->att('type') eq 'CTC') {
        $desc->first_child('descriptor')->first_child('mainterm')->pri
+nt();
    }
}
[download]

Please post valid XML.

Thanks so much for the help.<\p>
My xml file is too big to run. It has out of memory error now. My file size is about 1G.
Please help.