"I did test the CD on my wife's MacBook, CD player and DVD player, they all work perfectly. Do anyone has idea how to solve this problem."
Easiest way -- get Toast and use its option to "dupe" a music CD.
Or, try the freeware "Burn" app.
If that doesn't work you could try this:
1. Put the CD into your wife's MacBook
2. Extract the audio files to the internal hard drive
3. Burn the files to a NEW CDR blank.
4. See if that one now plays in YOUR MacBook.
To extract the audio, get QTAmateur:
http://www.mikeash.com/software/qtamateur/
Open each file one-by-one, and check options to make sure you are saving in 44.1khz, 16-bit, stereo, ".aif" format.
Save each file to disk, make sure you number them so they'll "line up right" when it's time to burn.
Once you have all the files extracted, drag them into an iTunes playlist and then burn them to a new CD.