The charity say more than 1,500 monkeys are brought into Britain every year, but they don't all make it alive.
Some die before they get out of the cages that bring them into the country, after three days of travelling.
The RSPCA demands include:
- An end to the import of monkeys
- A reduction in how many monkeys are used by scientists
- Shorter journeys for monkeys and better conditions to travel in
- An end to people being allowed to buy monkeys who are captured in the jungle
- Better conditions for all monkeys kept and used by scientists
The charity also says that it is silly that there are rules about how to transport animals that are going to be killed for food, but not animals that are to be used by scientists.
The RSPCA have sent their report to the government in the hope that they will begin moves to stop the transport of monkeys.