Joan Lee Cole Parke, 66, a former teacher who moved to the Washington area last year when her husband became assistant rector of The Falls Church Episcopal, died Friday at Fairfax Hospital. She had a heart ailment.

Mrs. Parke was born in Belfast, Ireland, the daughter of a former president of the Methodist Church in Ireland. She earned bachelor's degrees in biology and chemistry and a master's degree in biology from Trinity College in Dublin.

In 1940, she came to the United States on a traveling fellowship sponsored by the English-Speaking Union. Two years later, she married the Rev. John H. Parke. Before moving to Falls Church last August, she had accompanied her husband to parishes in California, Arizona, Virginia and Massachusetts and taught at a girl's preparatory school in Northfield, Mass.

Besides her husband, of Falls Church, survivors include three sons, Richard, also of Falls Church, David, of Fortuna, Calif., and Air Force Maj. Robert Parke, a flight surgeon stationed at Pease AFB, N.H.; a daughter, Emily Chase of Grantham, Pa.; a half-brother, Syndney J. Cole of Dublin, and four grandchildren.

The family suggests that expressions of sympathy be in the form of contributions in her name to The International Order of St. Luke the Physician, 1212 Wilmer Avenue, Richmond, 23227.