Could you be more specific? Psychologists and psychiatrists study the brain to a certain extent (neuropsychologists for example), neurologists are doctors who help fix problems with the brain, neural engineers also study and work with the brain. It depends on what you mean by study the brain.
Study of the brain is called Neuroscience and those who study is known as Neuroscientist. Neuropsychology is the study of the brain's structure & function. Need more information about the human brain, you can take help by visiting at
Neuroscientists. However, thats a pretty broad term. As Ty said many different specialists study the brain, and there are many aspects to this branch of science.
erm... if u mean like a doctor that specifically treats all ailments and conditions of the brain- thats a neurologist.