Obstetricians at the Washington Hospital Center have voted to end hospital privileges for three nurse-midwives who have been delivering babies there for the last 15 months.

The vote, taken by the department of obstetrics and gynecology on Oct. 7, went against the midwives even though obstetricians at the hospital said the three had had no complications and had been well accepted by patients and staff. Department members told the midwives that the vote reflected opposition to their practice of also delivering at home.

The midwives, who practice at the Maternity Center in Bethesda, began delivering some of their patients at the hospital center in July 1979 as a pilot project backed by several obstetricians on the staff. Dr. F. Norman Berry, who helped start the project, said its purpose was to make delivery by a nurse-midwife available in a hospital setting, thereby reducing home deliveries, which the obstetricians regard as risky.

A hospital representative said the vote, 21 to 12 in favor of revoking the privileges, represented only a recommendation, and would not be acted on unless approved by the medical board and board of trustees.

Janet Epstein, one of the three midwives, said she knew of no similar situation in which administrators had overruled a department's decision.

In the last decade, nurse midwives have gained popularity as an alternative to obstetricians among some patients, who believe they give more personal care and spend more time with women during pregancy and labor. At training programs like the one at Georgetown University, nurse-midwives learn to handle normal pregnancies and deliveries and to screen out patients with obstetrical or medical problems, whom they refer to doctors.

A number of nurse-midwives practice individually or in groups in the Washington area, many of them doing home deliveries exclusively. Some, such as those employed by Group Health Association, deliver their patients in hospitals.Those without hospital privileges arrange "backup" with an obstetrician who promises to admit a patient to the hospital if there are problems with a home delivery.

The vote at the Hospital Center reflects a difficulty midwives are having throughout the area: opposition from doctors who disapprove of their training, disagree with their practice of home deliveries, or fear their competition for patients.

Both Epstein and Berrys said they regarded the pilot program as a success.

Epstein said the midwives delivered only 35 patients the first year, but expected to deliver more than 100 during the second.

The hospital representative said the midwives would be allowed to finish delivering those patients already enrolled for a midwife delivery at the hospital.