Avid Media Composer is not available for Linux but there are plenty of alternatives that runs on Linux with similar functionality. The best Linux alternative is Kdenlive, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 50 alternatives to Avid Media Composer and 15 is available for Linux so hopefully you can find a suitable replacement. Other interesting Linux alternatives to Avid Media Composer are Shotcut (Free, Open Source), DaVinci Resolve (Freemium), Avidemux (Free, Open Source) and OpenShot (Free, Open Source).
Avidemux is a free video editor designed for simple cutting, filtering and encoding tasks. It supports many file types, including AVI, DVD compatible MPEG files, MP4 and ASF, using a variety of codecs. Tasks can be automated using projects, job queue and powerful scripting.