Browne was born in Turkey where her parents were missionaries with the American Board of Commissioners for Foreign Missions (ABCFM). Graduating from Mount Holyoke College in 1900, she was inspired by the Boxer Rebellion to set her sights for China. Students and alumnae of the school sponsored her missionary service. In 1903 she graduated from Hartford Theological Seminary in religious pedagogy and in 1905 sailed to China to take charge of a congregationa1ist girls' school. In 1913 she married ABCFM missionary evangelist Murray Scott Frame, but within five years she lost two children and had become widowed.
In 1918 she began to teach at the North China Union Women's College in Peking and became dean in 1922 after it affiliated with Yenching University. In 1928 the college was merged with the university. In 1931, after resigning under pressure to make way for a Chinese dean, Frame became secretary of religious education of the North China Congregational Church and undertook itinerant evangelism and rural education. In 1938 she attended the Madras Conference of the International Missionary Council as a delegate of the China Christian council. Her service in China was cut short by cancer.