Check the playing surface for defects and also hold the cd against a light to see if there's a scratch on the label side which lets light through.
It's not too surprising that a CD will work perfectly on one machine and skip on another -- there are variations in design and wear which mean that different decks perform differently.
This is a brand new cd. However, I cleaned the surface of my cd player with a q-tip and that worked so I quess it was my cd player. Thanks for your help.