Zimbabwean Prime Minister Robert Mugabe, on his first trip to the United States since he took power last April, is expected to meet with President Carter here next Wednesday to discuss the possibility of obtaining more economic assistance for his hard-pressed government.

Secretary of State Edmund S. Muskie will also host a lunch for the new black Zimbabwean leader during his one-day visit to Washington, according to State Department officials.

Mugabe was a coleader of the Black Nationalist Patriotic Front that led to the eight-year-long guerrilla war against the white settler regime in what was formerly known as Rhodesia. He describes himself as a Marxist, but so far has proven to be a moderate primarily interested in maintaining his country's stability and white confidence in his new and still fragile government.

He has also refused to allow the Soviet Union and its allies to open embassies in Salisbury in retaliation for their refusal to support his wing of the Patriotic Front during the war. Instead, he has turned to the West -- Britain and the United States in particular -- for diplomatic support and economic aid.

Mugabe's main purpose in coming to the United States is to address the United Nations General Assembly in New York after it formally admits Zimbabwe as its 153rd member early next week. He will also take part in the U.N. special economic debate that gets under way Monday.

Both State Department and Zimbabwean Embassy officials said in a meeting between Carter and Mugabe was anticipated but that the scheduling for it had yet to be worked out.

In his discussions with President Carter and Secretary of State Muskie, the new Zimbabwean leader is expected to ask for a considerable increase in U.S. economic assistance. He has already publicly expressed his disappointment with the present level of American aid following an earlier proposal by former Secretary of State Henry Kissinger of a $1 billion fund to help the country following its independence under an elected black government.

State Department officials said the U.S. aid package for Zimbabwe through September 1981 could amount to over $100 million in loans and grants, plus a possible additional $150 million in Export-Import Bank loans now under consideration.

Mugabe is also expected to present his formal thanks to President Carter for his personal efforts in helping to bring about elections ending the war in Zimbabwe on terms acceptable to the black nationalist guerrillas. Carter's refusal to recognize the short-lived, white-backed government of Bishop Abel Muzorewa, is widely regarded to have been a crucial element in its failure to gain Western acceptance in 1978-79.