Do I need to sterilize my baby sippy cup he s one year old, I use steam sterilizer to sterilize bottles?

Depends on Supply. This is really not necessary if you have a municipal water supply that is regarded as safe. Just wash it with soap in hot water as you wash the other dishes in the household. If you have a well water supply or unsafe water supply this is of course not the case and the cup should be sterilized.