I am planning to re-draw the wells completion schematic diagrams.The ones I have are old and not easily readable. Can any body advise on the computer program or software which is appropriate for the job?  

I'd recommend visio.  You can create a simple tubing stencil, then just keep over laying.  You can export or attch excel files with data like size, grade, threads, etc..

Petrofocus Completions Manager is the benchmark well completions package in the UK- every well diagram I've ever seen in the North Sea has been done with it.  I have no idea how much it costs though!

A quick google for well completions diagrams throws up various freeware you might want to use, and if you hunt around, you should be able to get a set of pitures of poackers, WEGs and so on to drop into excel so that you can use excell as dcasto says ... I did (and I might be able to work out how to post a link to them; but be patient- high technology can be confusing to a bloke who just makes holes in the ground!)

One of my friends once tried something called VIPR, it's an excel add-on that had hundreds of pictures, tubing, packers, etc... and let you select them and stack them to visually create the diagram you want. I don't know how much it costs but if you decide to go with Excel it might save you time searching for graphics.

hth