There are two possible reasons for this. One is that your puss is getting motion sickness from the mixed messages they're getting from their sensory organs. Their inner ears are telling them they're moving but their eyes don't see any movement. We sometimes get something similar if we read a book in the car. It may be worth trying a change in position of the carrier so your cat can see the world moving past. Anti-nausea medication from your vet can also help.
The other reason is anxiety. Usually carriers don't mean fun things for cats - they usually are on the way to the cattery or to the vet! Feliway is an anti-anxiety pheromone that can be safely sprayed around the carrier, and it would be a great idea to spend some time making the carrier a positive place for your puss. There are some great suggestions in this article - Cats And Carriers 101
If none of that helps, then again, an anti-anxiety medication prescribed by your vet may make the trips less stressful for them. | 10.26.15 @ 00:51