Thank all for your answers!!
I've tried all the ways you mentioned. like below:

# omit parameters

use strict;
use warnings;

use Net::Telnet;
open (STDERR, ">>err.log") or die "error!$!\n";

sub init{

    read_par();
    #telnet_login("sh /backup/auto_backup.sh > /backup/backup.log &");
    telnet_login("echo 1 >>1.txt"); #just a test
}
init();

my $tt = <STDIN>
sub telnet_login{
    my $command = shift;
    my $tl = Net::Telnet->new() or die "???\n";
    $tl->open($remote_server);
    $tl->login($username,$password);
     my @output = $tl->cmd($command);
     print STDERR %ENV;
}
[download]

But it still just flashed and don't retain the cmd window! moreover, there isn't any err.log in system after running.

It seems scheduled task just run perl command which has not any parameter, I guess.

I don't know why, fortunately, I find a easy way to walk around. activeperl has a tool named pl2bat to translate pl to bat. I just translate my snippet into bat and modify scheduled task configuration accordingly. It works!

Anyway, Thank monks again! and hope any gurus could figure out the reason invoke this strange issue.
UPDATE:
Thank andreas1234567 for pointing out typo.