In this digital world, we cannot say nothing is impossible, everything can be done in this era today. I was having a trouble in downloading Anyconnect on Ubuntu but now it will not be a problem anymore.
I was facing some real issues for installing on Ubuntu after a couple of tries and a hard work I was able to get my problem solved, I opened up the terminal and entered these list of commands and it was like a magic everything starts working properly. Must try if you are having the same issue.
Here is some easy way for installation of Cisco Anyconnect on ubuntu 18.04 follow these commands:

sudo apt-get update
sudo apt-get install network-manager-openconnect
sudo apt install libpangox-1.0-0
sudo apt-get install lib32z1 lib32ncurses5
cd ~ && mkdir download-anyconnect
cd download-anyconnect && wget
tar -xzvf anyconnect-predeploy-linux-64-4.3.05017-k9.tar.gz
cd /anyconnect-4.3.05017/vpn/
sudo ./

sudo systemctl daemon-reload

Security Warning: Untrusted VPN Server Certificate! AnyConnect cannot verify VPN server: serverName

After getting my problems solved with these commands I tried it with OneVPN which is fully compatible with Cisco anyconnect which provide a secure and fastest VPN service all around the world. As far as my opinion they are one of the best VPN service provider at cheap prices.