The week-old kid is smaller than a house cat, which owner Tony Scott says is a very rare sight.
Normally baby goats are about eight or nine inches tall, but this lively little animal is only five inches high.
Mr Scott who owns Scotty's Donkeys and Animal Park at Apley Farm Shop, in Shifnal, said Bill's mother was small so he was not surprised at his size.
"We expected him to be smaller than normal," he said.
"Bill's mother is very small so we were hoping the billy goat would be too."
Mr Scott added: "He is smaller than the average cat, which is very very rare for a goat.
"Now at a week old he is getting ready to make his debut over half term, when we reopen after being closed during the winter months.
"We think he will be very popular with the children when they come and visit this week.
"He is doing really well and we are really happy with his progress."
Mr Scott runs the animal park with his daughter Clare, and has done for the past four years.
Every year the business shuts at the end of November and reopens in February.
Mr Scott added: "We always close during the winter for a few months due to the weather.
"But we are open now and we expect Bill to be very popular.
"We have other animals here and we also have a very small lamb, which is very cute and fluffy, so I am sure that will also get some attention."