Linux has a few apps when it comes to Non-Linear Video Editing. Not as many as Windows, but enough to keep you entertained if your current choice dissatisfies. The first option and probably the easiest, is Avidemux.
Avidemux easy is designed for simple cutting, filtering and encoding tasks. It supports many different video media: AVI, DVD, MPEG-2, MP4, ASF, H.264, MPEG-4, QuickTime, 3GP, and more.
Output formats: AVI, H.264, MPEG, MPEG, MP4, etc. Avidemux includes a wide variety of codecs. You can cut, filter, encode movies. Avidemux has scripting capabilities, and supports the following video formats: DVD, VOB, AVI, DivX, XviD, WMV, MPG, MP4, AVI, Mov, Mkv, DV, Flv. Audio codecs: MP2, MP3, Vorbis, AAC, AC-3, WAV PCM, LPCM.
OpenShot a powerful open-sourced video editor for Linux. OpenShot can easily add sub-titles, transitions, and effects, and then export your film to DVD, YouTube, Vimeo, Xbox 360, and many other common formats.
Kdenlive an open-sourced editor for Linux and FreeBSD, which supports DV, AVCHD and HDV editing. Kdenlive uses open source projects, such as FFmpeg, the MLT video framework and Frei0r effects.
Kdenlive was designed for basic video editing to professional class work, and provides unique features that allow you to mix virtually any kind of media, such as video, audio and still images.
LiVES is simple but powerful video editor that's small in size and has many advanced features.
Mixing realtime video performance and non-linear editing. You can get started editing without worrying about formats, frame sizes, or framerates. A flexible tool for both VJ's and video editors - mixing and switching clips, trimming and editing using the multitrack timeline.
PiTiVi is a powerful video editor based on GStreamer and GTK+.
PiTiVi allows users to edit audio/video projects based on the GStreamer framework and allows almost any media file supported by GStreamer to be imported, along with projects using any supported container and codec combination.
PiTiVi provides several ways of creating a timeline from simple view full editing view.
Cinelerra is a really powerful video editor, not aimed at the casual or home user, but more at the professional.
Cinelerra includes support for high-fidelity audio and video. It is resolution and frame rate-independent, meaning that it can support video of any speed and size.
Cinefx is a playback, editing, encoding, animation and visual effects tool based on the Jahshaka technology that allows you to create professional digital media on your desktop. Use tools like hollywood uses to create great films and special effects.
VLMC from the people who brought you VLC the VideoLan Client, now comes VLMC the VideoLAN Movie Creator. A non-linear editing software for video creation based on libVLC and running on Linux, Windows and Mac OS X!
Finally, ZS4 Video Editor. ZS4 has many features. Here are a few: Unlimited number of audio, video and picture tracks. Unlimited number of video/audio effects for every track. Produce video with a resolution of 8x8 or 16000x16000 (~200 Megapixels / frame) and many sizes in between (custom). Full automation control for all track and effect variables using keyframes (cropping, zooming, panning, volume, rotation, opacity, key-color etc...). Full cross integration of audio and video. (noise gates triggering video effects. video brightness controlling volume etc.). Manipulate the flow of time, forward, backward, speed up and slow down smoothly. Grouping of video/audio tracks into sub-groups (submixers) which can then be manipulated (faded/rotated/effected etc) as if they were a single track.
Now go choose.