open (FILE_LIST, '/home/user/d/file_list.txt') or die "File list open fail: $!";

to make sure your open is successful - that would certainly explain your observation. Barring that, a quick review of Archive::Zip doesn't raise any more flags. Try modifying your while loop to:

while (<FILE_LIST>) {
    print;
    chomp;
    my $member = $zip->addFile($_);
    print "Add error" unless ($member);
}
[download]

and tell us if it actually outputs what you expect.

First of all, thanks for your reply :)

I have added print statement and it outputs the same of "cat" command:

my_script.pl
/home/user/a/a.txt
/home/user/b/b.txt
/home/user/c/c.txt
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and my zip file is still void :(

But if I put the three txt files (a.txt, b.txt, c.txt) in the same directory of perl script, then the script works as aspected and my zip file contains the three files

The only suggestion I can make is that in reformatting your information for posting, you have somehow removed your bug. Specifically, running the script:

#! /usr/bin/perl
use strict;
use warnings;
use Archive::Zip qw( :ERROR_CODES :CONSTANTS );

my $zip = Archive::Zip->new();

open (FILE_LIST, '/home/user/d/file_list.txt')  or die "File list open
+ fail: $!";

while (<FILE_LIST>) {
        chomp;
        my $member = $zip->addFile($_);
        print "Add error" unless ($member);
}

close FILE_LIST;

unless ($zip->writeToFileNamed('/home/user/d/backup.zip') == AZ_OK) {
        die "write error";}
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from multiple directories yielded success for me, with input file:

/home/user/a/a.txt
/home/user/b/b.txt
/home/user/c/c.txt
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and where success was measured by the results of the script:

#! /usr/bin/perl
use strict;
use warnings;
use Archive::Zip qw( :ERROR_CODES :CONSTANTS );

my $zip = Archive::Zip->new('backup.zip');
print $zip->memberNames();
[download]

where the only scrubbing I performed was changing user name. The only other suggestion I can make is that a review of the add_file method in Archive::Zip includes the admonition:

NOTE that you shouldn't (generally) use absolute path names in zip member names, as this will cause problems with some zip tools as well as introduce a security hole and make the zip harder to use.