Staff at the animal charity have described the deaths as ‘despicable’.
The RSPCA has hit out at people using airguns to target wildlife.
The charity was contacted on Wednesday morning after a woman found a goose collapsed in Wolverhampton Street.
Animal collection officer Cara Gibbon attended to try to help the bird.
She said: “The bird was walking when I arrived but kept slumping to the ground so I took him to a nearby vet where x-rays showed the poor thing had been shot with an airgun.
“Two others were found dead nearby so I suspect someone has come along and thought it would be funny to shoot at these birds.
“Why someone would want to harm these beautiful creatures is beyond me – I’m totally lost for words.”
The surviving goose remained at the vets for emergency treatment and care but died on Friday from her injuries.
The RSPCA has now launched an investigation and wants to find those responsible for killing the birds.
It comes after a Canada goose was found with a crossbow bolt through its head in Smethwick.
“It’s despicable that someone would deliberately attack these birds and shoot them and we’d like to find those responsible,” Ms Gibbon added.
“Anyone with any information about what happened should get in touch by calling our appeal line on 0300 123 8018 and leave me a message.
“Whilst there are some shooting practices which are legal, we would like to remind people that it is an offence under the Wildlife and Countryside Act to intentionally injure, kill or take a wild bird, except under licence.
“Anyone found guilty could face an unlimited fine and/or six months imprisonment.”