Firefighters from Penzance were called to three bins fires and a rubbish fire in a street junction between 11pm and 2pm.
None of the fires was serious and each was quickly contained.
Devon and Cornwall Police are treating all four fires as arson and believe they are connected.
They are also linking the fires - at Britons Hill, Coinagehall Street, the beach near New Street and in the road at St Mary's Street - with a small fire set on the bandstand in Morrab Gardens. That fire did not need firefighters to attend and was reported to police by garden staff.
Inspector Jean Phillips said officers were conducting door to door enquiries around the sites of the fires and urged anyone with any information to contact the police.
She said: "Whilst last night fires were confined to bins and rubbish there is always the worry that it will spread to neighbouring premises with people inside. Bins can be replaced but the potential is the worry."
Call Devon and Cornwall Police on 101 quoting crime reference AP121826 for the overnight fires and AP121816 for the fire in Morrab Gardens.
