Yes, some mother cats, also known as queens, will eat one or more of their kittens. There are a number of reasons why the queen might choose to do this, and this behavior is not necessarily a reflection of her inexperience as a mother.
When a mother cat feels threatened, either by humans or predators, and has no way to hide her kittens, she might choose to kill them to protect them. Queens will also kill kittens that have genetic defects or are weak as she does not want to waste her limited milk supply on caring for them. She may also eat these weaker kittens in an attempt to get some of her strength back after having given birth. If a kitten dies in the nest, she will eat it to prevent the decaying body from attracting predators or spreading disease among the remaining kittens.