A shrimp does have a brain as do all invertebrates. The brain works with the central nervous system, which ensures voluntary movements occur throughout the body.
In shrimp, the brain is connected to the brain by synapses, which pass electrical and chemical signals to cells throughout the body.
The nervous system in invertebrates is actually quite complex and is made up for four individual parts that work together as a team. These are the suboesophageal ganglion, the ganglia, the ventral nerve cord, and, lastly, the brain itself.