You can use iMovie Video Converter to convert AVI to videos supported by iMovie such as MP4.
Step 1: Install and Run iMovie Video Converter for Mac
You can download the trial version here: http://www.mp4kits.com/Guides/iMovie/import-avi-to-imovie/
To install it, simply mount the .dmg archive by double-clicking it, and copy the application to your applications folder (or wherever you want it).
Step 2: Add AVI Video
Click “Load video" button to add video files for converting. After one or several video files like AVI, WMV, 3GP, etc are imported successfully, you can see
all of them listed in the program.

Step 3: Output Settings
Choose a format like MP4 which is compatible with iMovie from the profile drop-down menu.

Step 4: Start convert AVI to iMovie MP4
Press "Convert" button, it begins to convert your AVI files to iMovie MP4 format.

After the conversion, you can right-click in the Event Library area and choose Import Movies to import the created .MP4 file to your iMovie project. Specify
a new Event name if desired. The imported video will now be available for you to edit.
avi to iMovie converter can also import flv to iMovie, import 3gp to iMovie, import asf to iMovie, import 3g2 to iMovie, import mkv to iMovie, import mod to iMovie, import tod to iMovie, import mts to iMovie, import m2ts to iMovie, import tp to iMovie, import trp to iMovie, import ts to iMovie, import m4v to iMovie, import wmv to iMovie

How to import DVD to iMovie for edit
Apple’s iMovie is part of the iLife suite of software products that comes free with every Mac. The iLife apps are designed to enhance users digital lives by making playing and working with digital media easy for all users. As its name suggests, iMovie is about about video editing.
Before you can begin working in iMovie, you need to bring in some video from a video recording device and store the video on your computer (or an external hard disk). iMovie will also allow you to import the following file formats:
DV (standard definition) and HDV (high definition)
MPEG-2 and AVCHD from Camcorders
MPEG-4, DV, and .MOV files stored in Mac
Please note that DVD is not supported, so importing a DVD to iMovie is not a straightforward process. In this situation, third party software – DVD to iMovie Converter help you convert DVD to the formats that are compatible with iMovie. You can convert DVD to MOV (*.MOV), MPEG-2 Movie (*.MPG) or MPEG-4 Movie (*.MP4) as followed several steps.
Step 1: Install and Run DVD to iMovie Converter for Mac
You can download the trial version here: http://www.mp4kits.com/Guides/iMovie/import-dvd-to-imovie/
To install it, simply mount the .dmg archive by double-clicking it, and copy the application to your applications folder (or wherever you want it).
Step 2: Load DVD movies
Insert DVD disk into DVD drive .Click Load DVD button (Or click Load IFO button) to load your DVD.
Step 3: Output Settings
Choose a format like MOV which is compatible with iMovie from the profile drop-down menu.
Step 4: Start convert DVD to iMovie MOV
Press "Convert" button, it begins to convert your DVD to iMovie MOV format.
After the conversion, you can right-click in the Event Library area and choose Import Movies to import the created .MOV file to your iMovie project. Specify a new Event name if desired. The imported video will now be available for you to edit.
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