The designing of mobile app icon can become a daunting task. It is even more frustrating as many of the online creation websites charges for downloading the .png files. After quite a bit of researching, I stumbled upon an open source software to make the app icon, Inkscape.
Download the Inkscape software from the official website.
The app has lot of features and you might be confused if you start searching for tutorials on Youtube. Many of them are good but they go into basics and unwanted stuffs for creating an app icon. You can go through them if you want to completely understand the design process.
Here is a YouTube video for Inkscape. This video has concentrated specifically on how to create a mobile app icon.