A goose died and another was left seriously injured after being shot at the Mill Pond in Storrington.
The white geese were found with head and neck injuries at the pond in Mill Lane.
Details of the incident, which happened on Monday, have only just been released by the RSPCA.
Inspectors collected the geese and took them to a nearby vet, but one had such serious injuries it had to be put down.
Vets treated the other goose and it is now recovering at Brent Lodge wildlife sanctuary, Sidlesham, near Chichester.
RSPCA inspector Tony Pritchard said: "We would like to find out who shot these geese.
"It is illegal to shoot and injure birds in this way and cause them unnecessary suffering."
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