Curran studied at the National Academy of Design, under Walter Satterlee, and the Art Students League. At age 23, he had his first public exhibition at the Academy. From 1889 to 1891, Curran studied at the Académie Julian in Paris, where he studied with Benjamin Constant and Jules Joseph Lefebvre. He won an award at the Paris Salon of 1890. He also won prizes at the Columbian Exposition of 1893 in Chicago, the Paris Exposition of 1900, and the 1901 Pan-American Exposition in Buffalo, New York.
Curran is best known for his paintings of female figures posed within picturesque vistas of the Cragsmoor area, and usually rendered in an impressionist style. The “new” women of these paintings embodied health and vigor. He also painted genre scenes, portraits and landscapes.