The third system and first severe tropical cyclone of the 1978–79 season, Peter developed on 29 December from a weak low pressure area over the Gulf of Carpentaria.

While trekking slowly offshore the east coast of Queensland, the storm dropped very heavy rainfall, peaking at 1,947 millimetres (76.7 in) at Mount Bellenden Ker, making it the wettest tropical cyclone on record in Australia at the time.

[2] The system was subsequently considered to have peaked as a Category 2 tropical cyclone on 31 December, with 10-minute sustained winds estimated at 110 km/h (70 mph) by the BoM.

[2] Several hours later, the system made landfall between Aurukun and the Edward River mission, Queensland, at around 20:00 (Australian Eastern Standard Time, 11:00 UTC).

[3] As Peter made landfall during 31 December winds of 120 km/h (75 mph), were reported from both Fitzroy Island and the Edward River mission weather stations.

[1] The strongest observed winds in the territory was 74 km/h (46 mph) on Northeast Island, while the highest precipitation total was 140 millimetres (5.5 in) in Nhulunbuy, 107 mm (4.2 in) of which fell in 24 hours.

[2] In Queensland, the Brisbane TCWC issued cyclone watches and flood warnings as the storm passed over the Cape York Peninsula.

[1] The storm dropped very heavy rainfall while drifting offshore Queensland, with Mount Bellenden Ker recording 1,947 mm (76.7 in) over a period of approximately three days, making Peter the wettest tropical cyclone in Australia at the time.

[20] Emergency personnel crews were put on standby in Innisfail as water up to 60 cm (24 in) threatened dozens of homes in the eastern part of town.

Additionally, a policeman was winched by helicopter to deliver food supplies to 10 isolated people on 7 January in Goldsborough, which is located in the Gillies Range to the west of Gordonvale.

About week later, the Cabinet supported a measure by Minister for Primary Industries, Vic Sullivan, to offer low-interest loans to farmer who lost significant amounts of crops and livestock.