The seventh named storm of the 1978 Atlantic hurricane season, Greta formed from a tropical wave just northwest of Trinidad on September 13, and despite being in a climatologically unfavorable area, gradually intensified while moving west-northwestward.

On September 19, it made landfall on Belize near Dangriga and quickly weakened into a tropical depression while crossing Guatemala and southeastern Mexico.

Taking a similar path to Hurricane Fifi four years prior, Greta threatened to reproduce the devastating effects of the catastrophic storm; however, damage and loss of life was significantly less than feared.

Later that day, it is estimated the system developed into a tropical depression about 75 mi (121 km) west-northwest of Trinidad, based on ship and land reports.

At 0710 UTC on September 18, the Hurricane hunters observed a minimum pressure of 947 mbar (28.0 inHg) just off the northern Honduras coast, which was the basis for the estimated peak intensity of 130 mph (210 km/h).

[7] After passing through the Bay Islands off northern Honduras,[5] Greta weakened slightly while approaching Belize, and made landfall near Dangriga at 00:00 UTC on September 19,[4] with winds of about 110 mph (180 km/h).

A large high pressure area from the Carolinas to the central Gulf of Mexico turned Greta southwestward toward the eastern Pacific Ocean.

[9] At 00:00 UTC on September 20, the Eastern Pacific Hurricane Center (EPHC) took over responsibility for issuing advisories while Greta was 30 mi (48 km) from the coast.

Based on observations from nearby ships and radar, it is estimated Olivia attained minimal hurricane status early on September 22.

While tracking towards the Mexican coastline, the system weakened below hurricane threshold; between 19:00 and 20:00 UTC, Olivia made landfall about 60 mi (97 km) east of Salina Cruz.

[6][11] Early in its duration, Greta produced heavy rainfall in the Netherlands Antilles, but the strongest winds remained north of the island.

[1] Late on September 17 when Greta's eye was just offshore Honduras, the country's government issued a hurricane warning for the eastern coastline.

[14] The Honduran government put its military, police, and Red Cross on standby in advance of the storm, due to fears of a repeat of Hurricane Fifi in 1974.

[19] There was one death in Honduras,[9] and nationwide, the hurricane damaged about 1,200 homes, washed out roads and bridges, and wrecked coconut and rice crops.

The Tactical Air Command had sent two squadrons to Central America in the middle of 1978, and in response to the request from Honduras, two aircraft delivered over 100,000 lb (45,000 kg) of cots, water, and generators; the units also deployed a 13–person crew who specialized in disaster relief.

[20] In late October 1978, the United Methodist Church sent books and other supplies via aircraft to Belize, after a youth group rode out the storm there and desired to help residents.